Dark Matter vs. Modified Gravity: A Trialogue

It’s well known that all of our evidence for dark matter (and dark energy too, but that’s not the subject here) at the present time is indirect: it comes from observing the gravitational influence of the hypothetical stuff, not from detecting it “directly” (i.e., using some interaction other than gravitational). So it’s natural to ask whether we can do away with dark matter by positing some modification of the behavior of gravity; I’ve certainly wondered that myself.

And it may very well turn out that the behavior of gravity on large scales does not precisely match the prediction of ordinary general relativity. Nevertheless, I think that by now we’ve accumulated enough data to conclude that the universe cannot be explained solely by modifying gravity; there is ample evidence of gravitational forces pointing in directions where there isn’t any (ordinary) “stuff” to create them, leading us to accept the existence of some form of dark matter. About a year ago I put up a post that explained this point of view, and took aim in particular at the popular framework known as MOND.

This led to some good discussion in the comments, and also to a behind-the-scenes email exchange between Rainer Plaga, Stacy McGaugh, and me. It’s a bit of old news, but I thought there would still be some interest in our discussion, so (with permission) I’m posting our emails here. Seeing how the sausage is made, as it were. It’s a bit of a long read, sorry about that.


Rainer, March 1:

Dear Sean,

I discussed your recent vigorous defense of CDM your blog with Stacy, and he encouraged me to send you my – absolutely objective ;-) – position.

On the one hand I am with you that if Stacy uses terms like “serious fine-tuning problem for LCDM” in his newest paper’s abstract (which are then interpreted by science journalists in the way you exhibit), he had to quantitatively compare the expected properties of galaxies under the assumption of LambdaCDM with his data set. If he wants to criticise an idea he has to deal with the idea not with alternatives to it. Alas, he does not do that in this paper.

On the other hand I strongly disagree out of principle to require statements like: ?of course we have more than sufficient evidence to conclude that dark matter exists, we?re just trying to understand how it works and what else might be going on.? from anybody. Really Sean, this sounds like a caricature of the holy inquisition to me, “philosophers can speculate as long as they accept that the final truth is already known from the holy scriptures ;-)”.

Your statement: “Dark matter is real … there’s no reasonable doubt about the dark matter.” is misleading. Stacy and I of course know that dark matter in the form of massive neutrinos does exist beyond reasonable doubt. But that does not answer a crucial question. Crucial questions are: what flattens the rotation curves in galaxies? What creates the third CMB peak? CDM, MOND or something else?

In my opinion the final verdict on these questions is not in, yet. Allow me to argue why your top 3 arguments for the existence of CDM do not convince me, perhaps yet.

1. “MOND is ugly”: The alternative is not “theory for MOND” vs. GR but “theory for MOND” vs. GR + “theory for CDM particle”. The number of exhibited equations then becomes similar. How do you know that TeVeS is uglier than the “theory for CDM particle”?

2. “Clusters require DM anyway” If one could make a case that they require nonbaryonic cold dark matter, I would consider the case settled in favour of CDM. However, the dark matter required for MOND in clusters might be the ca. 40% fraction of baryonic matter that we anyway know is currently missing in clusters (even in LCDM). Do we agree? How can the argument be clinching then?

3. Your strongest argument is the one from the CMB. But still, replacing “MOND” with “CDM”, couldn’t your statement:

“Can some clever theorist tweak things so that there?s a MOND version that actually fits? Probably. Or we could just accept what the data are telling us.”

be used just as well to comment on the well known problems of CDM to reproduce the detailed properties of galaxies?

Wouldn’t this be a great topic for another “great debate” a la Shapley/Curtis 1920 between u and Stacy? In that case it turned out both were partly right and wrong, my personal bet: it would be the same this time ;-).


Sean, March 1:

Hi Rainer–

Ten years ago, it was perfectly respectable to speculate that there was no such thing as dark matter, just a modification of gravity. (It couldn’t have been MOND alone, which was ruled out by clusters, but it could have been some more elaborate modification.) That’s no longer true. The Bulltet Cluster and the CMB both provide straightforward evidence that there is gravity pointing in the direction of something other than the ordinary matter. The source for that gravity is “dark matter.” It could be simple, like an axion or a thermal relic, or it could be quite baroque, like TeVeS + sprinkles of other dark matter as required, but it’s definitely there.

If people want to contemplate that there is dark matter and also a modification of gravity, that’s fine. If people want to point to features of galaxy/cluster phenomenology and say that these features must be explained, that’s absolutely fine. But if people want to cling to the possibility that dark matter doesn’t exist, that’s not being appropriately cautious, it’s just ignoring the data, and it’s a disservice to the public to pretend otherwise.


Rainer, March 2:

Dear Sean,

I do not fully understand your argument: do you argue that the bullet cluster proves that _nonbaryonic_ DM exists? To me Stacy’s argument – that MOND might work only with the baryonic cluster DM which is an additional problem even within LCDM – cannot be currently excluded (see 2. in my previous e-mail). Do you disagree with his argument, and if yes, why?

For your convenience let me summarize Stacy’s general argument in my own words (Stacy please protest if I misrepresent it):

a. even within LCDM generally uncontested facts are that in clusters of the size of the bullet cluster (< 10(13) M_sun):
1. ca. 50% of the cluster's _baryonic_ matter is probably in some invisible form
2. the hot gas is a minor component of the total baryonic matter (see e.g. fig.1 here: http://arxiv.org/abs/1007.1980)

b. suppose that this baryonic cluster DM is in some non-collisional form (e.g. jupiters). Then a.1. would quantitatively explain MOND’s missing cluster DM and a.2. the observational fact that the bullet’s cluster mass is concentrated on the galaxies and not the hot gas.

It is somewhat paradoxical, but seems clear: if you want to rule out MOND you have to deal with its details, if Stacy wants to rule out CDM he has to deal with its details. Neither of you guys is really doing this, and I can understand why: both of you would feel you are wasting time on a wrong concept. But you would not ;-).


Sean, March 2:

Hi Rainer–

We know how much baryonic matter there is from BBN. It’s not enough to explain the Bullet Cluster or the CMB, even with MOND. Not to mention that you would have to come up with some way to turn the large majority of baryonic matter into some collisionless form. (The paper you just cited says ” the baryons are not missing, they are simply located in cluster outskirts” right there in the abstract.)


Rainer, March 2:

Hi Sean,

We know how much baryonic matter there is from BBN. It’s not enough to explain the Bullet Cluster or the CMB, even with MOND.

They claim ca. a factor 2 more dark baryonic matter than seen is needed in the clusters. What problem would that pose with BBN? (Don’t forget that the baryonic matter/CDM ratios derived from LCDM in clusters are meaningless if MOND were the answer).

Not to mention that you would have to come up with some way to turn the large majority of baryonic matter into some collisionless form.

Yes, this would need some ad-hoc gastrophysics to produce enormous amounts of e.g. jupiters especially in the cluster centre. Not nice, but not impossible, cooling flows etc… But if all that were true, the bullet cluster would be OK.

(The paper you just cited says ” the baryons are not missing, they are simply located in cluster outskirts” right there in the abstract.)

But that’s exactly what is needed also for MOND: the dark baryons are really hiding somewhere… They are not claiming a detection of these baryons! But let us take a step back on this paper:

What it discusses is the fact that clusters need some dark baryonic matter even in LCDM, ca. 30% of the baryonic matter is apparently unseen. This was unexpected, some gastrophysics will be needed to explain it. (They mention “AGN feedack” and stuff…)

MOND’s problem is more severe, ca. 70% of the baryonic mater would apparently be unseen in the central parts of the clusters. This was unexpected some gastrophysics will be needed to explain it.

Sorry, Sean, this seems like an open problem to me both for LCDM and MOND, admittedly a bigger one for MOND (but then clusters are their worst problem…), but not the ultraclean evidence for CDM that you are claiming…


Stacy, March 2:

OK, I think at least we all agree that BBN tells us the baryon density of the universe. Lets deal with one thing at a time, the dark matter in clusters. If I understand you, you are saying MOND is falsified because there is dark matter in clusters. Rainer is suggesting that a logical way out of this is if the excess mass in clusters is in some dark, baryonic, collisionless form. I agree it is tough to imagine what that would be (and have consistently said as much) but I am not willing to grant that I know it to be impossible. So the real leap to falsify MOND is to say that the dark mass in clusters is not just dark baryons, but WIMPs (or whatever non-baryonic particles compose CDM). And that follows how? Because Omega_m > Omega_b?


Sean, March 3:

MOND without non-baryonic DM is falsified by clusters, because you can’t fit them with the baryons implied by BBN regardless of what form they take. That’s admitted by most people, e.g. Sanders’ paper.

More interesting is the question of whether you could get around the need for non-baryonic DM with some other theory of modified gravity. The Bullet Cluster and CMB, again to most people, imply not. Could you wriggle out of that conclusion by combining some new as-yet-unformulated modification of gravity with a huge population of mysterious intergalactic Jupiters? No, because you would still be completely wrong on the CMB. It’s time to accept what the data are telling us and move on.


Stacy, March 3:

MOND without non-baryonic DM is falsified by clusters, because you can’t fit them with the baryons implied by BBN regardless of what form they take. That’s admitted by most people, e.g. Sanders’ paper.

Ah. I thought this was the conceptual error you were making. Clusters you certainly could fit just with baryons. They’re rare systems. If that is the only place we need dark baryons, then do the integrals. You can satisfy the residual mass discrepancy in clusters in MOND without making much dent in the BBN missing baryon budget.

Do I *like* such a solution? Certainly not. Neither do I like that fact that clusters are the only systems that come close to having the right baryon content in LCDM. Whay are galaxies missing more than half of their baryons? Dwarfs > 90%? I can imagine how this might happen, but the solutions are comparably contrived. The more basic point is that I am not willing to condemn a theory for needing some dark baryons if its competitor also needs dark baryons.

More interesting is the question of whether you could get around the need for non-baryonic DM with some other theory of modified gravity. The Bullet Cluster and CMB, again to most people, imply not. Could you wriggle out of that conclusion by combining some new as-yet-unformulated modification of gravity with a huge population of mysterious intergalactic Jupiters? No, because you would still be completely wrong on the CMB. It’s time to accept what the data are telling us and move on.

The CMB is really interesting. I correctly predicted the amplitude of the second peak (a prediction that is still quantitatively correct) by making the ansatz that there was whatever generally covariant theory might grow out of MOND looked just like GR in the early universe. Obviously that has to change later in order to grow structure, but at least it gives some proxy for what MOND might do with the CMB. At the time, I discussed some of the ways in which this would inevitably fail.

The response initially was that MOND itself made no prediction for the CMB, therefore we should disregard the chance success of this prediction. Now you want to treat the low third peak as an absolute prediction of MOND. You can’t have it both ways. Which is it?

A low third peak would have falsified LCDM. It survives that test. That does not automatically falisify MOND. It just means that the relativistic parent theory (whatever that might be – it is not obvious to me it has to be TeVeS) has to have a net forcing term a la CDM. Does that seem reasonable to me? No, and (as I said with the ultrafaint dwarfs) I too was ready to write off MOND on this point. But Skordis & Ferreira showed that the scalar field in TeVeS might have just such an effect. So I can not, in good conscience, say it is impossible.

You should not accuse me of ignoring data. I have written papers on these subjects. Indeed, one of the things that surprised and impressed me about MOND, when I first got over my initial revulsion and started to look into it, was what a great breadth and wealth of data it did quite in explaining. From the tone of your statements, I imagine you have no idea what I’m talking about. You really ought to check your facts before making ignorant statements to the effect that “MOND only does rotation curves.”

Indeed, you yourself appear to be ignoring facts. Why do any MOND predictions come true? Let’s suppose it is only true that all MOND does is fit rotation curves. That demands an explanation – one you nowhere attempt to provide. Your reasoning appears to boil down to “We’re sure that CDM exists, so somehow it must work out.” Well, I’ve tried – very hard – to see how it could work out. It aint easy. I won’t say it is impossible. But it is as absurd as some of the above dodges are with MOND. Dark matter in galaxies is like epicycles – you can fit anything you like, but it doesn’t explain why a simple formula does better.

You may find it hard to believe, but I started from exactly the same perspective as you. I am far more comfortable with CDM than with MOND. I will breathe a great sigh of relief if and when WIMPs are detected in the laboratory. Then we’ll know the answer, and we won’t have to have these bitter debates. However, I am not being unreasonable in holding the theory to a high standard of proof. If you want to convince me that, for sure, the universe is filled with some till-now hypothetical particle from a hypothetical dark sector outside of the Standard Model of particle physics, then show me a piece. Until then, you are over-reaching.


Sean, March 3:

You can’t just wave your hands and say that a mysterious “forcing term” will help explain the CMB. If there is no non-baryonic dark matter, there is no way that even-numbered peaks can be different from odd-numbered peaks; the configuration of baryons is precisely analogous. You can mimic the situation in TeVeS (although the numbers don’t seem to work out) because you’ve introduced an independently propagating scalar degree of freedom whose energy density doesn’t follow the baryons. You can give that scalar whatever name you like, but it is “non-baryonic dark matter.” A particularly contrived version, but that’s what it is.

You can’t explain the third peak without a source for gravity that propagates independently of the baryons.


Rainer, March 3:

MOND without non-baryonic DM is falsified by clusters, because you can’t fit them with the baryons implied by BBN regardless of what form they take.

Why is that? I just don’t get it, and am very open to be persuaded. 90% of all cosmic baryons are presently undetected, right? Only a fraction of the baryonic matter we see directly is in clusters (O(a few percent), let’s say 10%) So why can’t a small fraction, say O(2%), of all the cosmic dark baryons be in the form of e.g. jupiters in the central parts of clusters? They and stars would then dominate the cluster mass and be dissipationless —> no problem with the bullet cluster in MOND.

That’s admitted by most people, e.g. Sanders’ paper.

Where? In http://arxiv.org/abs/astro-ph/0703590 he states about cluster dark matter in MOND: “For example, there are more than enough undetected baryons to make up the missing dark component; they need only be present in some non-dissipative form which is difficult to observe.”

He also likes massive neutrinos, but not to the exclusion of baryonic dark matter.


Stacy, March 4:

Hi Sean,

OK, now we are discussing science again.

I take your point about the CMB very seriously. It seems to me that you are putting a lot of weight on the third peak, which is not all THAT well constrained. WMAP really has to scrape to get there, so the result is dominated by the systematics of PSF modeling. I presume they’ve done that right, but there are double exponential corrections involved in subtracting the foreground and then getting back to the cosmic signal, so they don’t have to go far wrong to make a bad mistake with the third peak. Presumably PLANCK will clarify this soon, though a glance at their first release images does not provide a lot of confidence about the foreground MW masks that WMAP used. I also wonder, given the visceral reaction you and others have at any suggestion that LCDM might be questionsed, if the PLANCK team would let themselves admit a low third peak even if the saw it.

For now, we have an apparently clear detection of a high third peak in WMAP, and we need to explain the data we have rather than the data we hope soon to have. And honestly, I expect the most likely outcome to be a confirmation of WMAP, with only minor tweaks. So we have to understand the third peak along with clusters and rotation curves and dwarf spheroidals and everything else.

I freely admit that I don’t know how to make the third peak high. I also don’t know that a high-ish thrid peak can’t be obtained in a more general theory. I agree with your point that pure baryons shouldn’t do that – the vector is wrong, as you say. I’m not even convinced TeVeS can do it. But lots of theories (not just MOND-inspired ones) invoke scalar fields, so I can’t exclude the possibility.

I also agree that this is contrived. But we are WAY into contrivance with LCDM, a point I believe you’ve made yourself on occassion. We’ve just gotten familiar with the contrived parts so that they no longer bother us. That doesn’t make them any less contrived.

You make the point that the scalar field solution in TeVeS is just a contrived form of non-baryonic dark matter. But even in pure GR we could use some form of non-baryonic dark matter that gives us the MOND phenomenology. Why not consider an effect due to the physical nature of the particles? Until we detect WIMPs, surely you at least agree that we don’t really know what the dark matter is?

I know everybody invokes feedback to “fix” galaxies, but those models are just as contrived. Actually, they are considerably more contrived, as they inevitably require many more parameters, and those parameters are simply tuned to match observations. Any competent theorist can tune any model to fit a given set of data.

I must have said this to you before, but I will say it again. The MOND formula provides an apparently correct description of the effective force law in galaxies. How does the dark matter “know” to arrange itself just so as to look like MOND? If it manages this trick in galaxies, why not in the solar system? How would we know that the solar system isn’t really run by an inverse-cube force law, but there is dark matter arranged just so as to make it look like an inverse-square law?

Could anything be more contrived?


Sean, March 6:

Hi Stacy–

I’m not sure what you are saying about the third peak in the CMB. We agree that “pure baryons shouldn’t do that.” I can only think of three possibilities.

(1) There is some sort of source for gravity other than baryons.
(2) There is a modification of gravity that doesn’t include new sources, but also doesn’t respond directly to where the sources actually are.
(3) The data aren’t good enough to say that the odd-numbered peaks are boosted relative to what we would expect from damped oscillations of baryons alone.

If it’s (1), then that’s non-baryonic dark matter and we should just admit it. I think that (2) is physically implausible, and as far as I know nobody has suggested otherwise. And I think that the time is past when anyone could credibly hang on to (3). Here’s a relatively recent figure (2 years ago) from Ned Wright’s web site.

Am I missing a possibility, or would you buy one of these three?


Stacy, March 7:

Hi Sean,

I basically agree with the 3 possibilities you list. Indeed, I thought that was pretty much what I said.

You imply that it is hanging on to vain hope to explain the third peak of the CMB by anything other than a new source. I am saying that it is a vain hope to imagine that turning the crank on any number of CDM numerical simulations is ever going to spit out the observed MONDian phenomenology. Just because LCDM works for the CMB does not automatically guarantee that it’ll work in galaxies, any more than MOND’s success in galaxies means it must inevitably succeed as a the basis of a cosmological theory.

There is a very simple empirical result in the data for galaxies that cosmologists have, by and large, simply ignored. The stated excuse is usually something like “well, galaxies are complicated, non-linear structures” and so we should be excused from explaining them. Indeed, in LCDM galaxies probably should be complicated. But they’re not. They’re simple. So simple, the obey a single effective force law. Fitting that with dark matter is like fitting epicylces to planetary orbits. Of course you can do it – you have an infinite number of free parameters. But it don’t make no sense.

I have said for years now that they conclusion you come to depends on how you weigh the evidence. The CMB is an important piece of that evidence. So are rotation curves. It is not obvious to me that the third peak should count 100% and galaxies zero. Yet that is in effect the weighting that lots of people appear to be using.


Sean, March 8:

Hi Stacy–

I think we’ve reached the end of what needs to be said. You agree with my three possibilities, and you agree (I think) that the CMB data are good enough to draw some conclusions. It comes down to whether you are willing to entertain the possibility that there is a mysterious new force that does not involve any new sources, yet also does not respond directly to where the actual sources are. (And in the process reproduces exactly what we would see if there were CDM.) You may think that is plausible — I, and most people in the field, do not. Therefore, we believe that there is non-baryonic DM, and the question is how it behaves.

You seem to think I am defending LCDM, when I have never mentioned it. I am defending the claim that “non-baryonic dark matter exists.” As I said in the original post, we certainly have to explain the phenomenology of galaxies and clusters, and the right explanation may very well involve a modification of gravity or interesting new physics in the dark sector — both of which I’ve written papers about. Nobody is suggesting that we ignore data from galaxies and clusters. But none of that data straightforwardly implies “non-baryonic dark matter does not exist.” It’s a complicated dynamical problem. The CMB — an enormously simpler system, where everything is in the linear regime — does straightforwardly imply “non-baryonic dark matter exists.” Admitting that will improve our chances for future progress.


Stacy, March 8:

Yes, we’ve said what we’re going to say. But you still don’t seem to get it. The CMB is simple. It is not enormously simpler. Galaxies are also simple. One must invoke absurdly complex mechanisms to make that happen. The argument against dark matter doing this boils down to fine tuning. I don’t like fine tuning problems, especially when a theory is not otherwise falsifiable (e.g., epicycles). Note that as you claim not to be specifically defending LCDM, I am not specifically defending MOND. There is an empirical phenomenology that constitutes a fine tuning problem for ANY dark matter picture (that does not some how build it in).

Since we can’t explicitly falsify the existence of dark matter, what could be worse than this mother of all fine-tuning problems? I understand the implausibility of what you are saying in the CMB, but you seem to miss the same kind of point in galaxies. I worry that we won’t find WIMPs and keep pursuing other DM candidates indefinitely – how do we know when to stop? How would this be different from another millenium of dark epicycles?


Rainer, March 18:

Dear disputants,

Thanks for this really informative and nearly polemic free (Stacy please stop blaming your colleagues to construct epicycles ;-)) debate!

To me (and it seems also to Stacy) Sean’s concentration on his main argument, makes his case for some kind of “dark non-baryonic field that enters the stress-energy tensor in GR” quite convincing. It then stands to reason (but is not absolutely necessary) to identify it with a quantum field for some new massive particle.

If I may make Stacy’s main point in my own words: galaxies are observed to be simpler than they would be expected to be: at least a large fraction of them obeys a strange simple MOND rule, which is without a simple plausible motivation in known physics. In addition there are indications that galaxies sometimes behave in ways that they should not in LCDM (tidal dwarves should not contain dark matter but they seem to do).

This reminds one of atoms in classical physics, which were expected to show a very complex behaviour but obeyed strange simple rules, sometimes in contradiction to the known physical laws at the time. The old quantum condition comes to mind as somewhat analogous to MOND’s law of motion. Initially it was attempted to explain these rules within the known concepts, and that was all right and necessary.

But, as quantum mechanics showed, there is _also_ the possibility that strange simple rules for basic objects of the theory are first clues for really new concepts.

Sean, don’t you have at least a little bit of sympathy for this possibility?

I close with following proposal: CDM or MOND? is not a good question. A better question is: are the successes of the MOND rule _perhaps_ a first clue to new concepts which will modify our understanding of the “dark non-baryonic field that enters the stress-energy tensor in GR” in the sense that it is not only a new quantum field within standard QFT?


Sean, March 18:

Hi Rainer–

Sure, I’m happy to agree with that. In fact, you will find exactly those sentiments way back in my original blog post on the topic. I just think we’re past the point where we can conclude that non-baryonic dark matter exists — what form it takes, how it interacts, and what additional things might be going on, are all crucially important questions. Of course DM faces important challenges from the phenomenology of complex structures, and that should be taken seriously; but no-DM alternatives are ruled out by the data, which should also be taken seriously.


Stacy, March 19:

Science is dead.


  1. It’s a bit of a long read, sorry about that.

    Well, one major reason that it’s a long read could be that you included the whole debate *two* times… ;-)

  2. Nice … but in cutting and pasting, you included the whole trialog twice.
    Midway, after Stacy’s science is dead, you start at the beginning again.

    Side note: Since epicycles were the addition of circular motions on top of circular motion applied for no reason except to make observations predictable using tools already in the chest (circular trig functions)… it seems ironic that the MoND proponent would be accusing the CDM proponent of using epicycles. MoND is clearly the arbitrary formula fits the pattern plan here.

  3. I think the time is ripe to actually revisit the MOND RC fits. MOND sometimes claims “no free parameters” for rotation curve fitting, but for individual galaxies it is standard practice to let the distance and the stellar mass-to-light ratio vary when fitting the rotation curve. However, within ~4Mpc, we have many galaxies that now have excellent stellar population data, which both nail down the distances to 10%, and place good constraints on M/L and its radial variation. Many of these also have high resolution HI and CO imaging, giving a good handle on the gas. They also have Spitzer 3.6micron imaging, for which the M/L variations should be intrinsically smaller than traditional B-band M/L. In short, one is no longer free to vary these quantities arbitrarily.

    I’ve long been curious about how well MOND will hold up in these circumstances.

  4. As an impartial observer it seems to me Stacy basically just misunderstood Sean’s original point as being LCDM vs MOND when all he was saying is that there must be non-baryonic dark matter.

    Since you both agree that the third peak requires some non-baryonic explanation even within MOND scenario, Sean’s original and only point is correct that the evidence is clear for some form of matter that can’t be baryonic whatever else there might be out there including modified forces.

  5. Non- baryonic dark matter makes sense of the data observed. MOND is unnecessary as we know that it does not work for clusters. It is just a matter of time before we gather direct evidence in detecting DM. Very exciting time for physics these days.

  6. The following quote from Stacy McGaugh suggests a potentially serious misunderstanding of the way science works. In the process, I think it illustrates the key psychological “trap” that is slowly exiling many MOND advocates from their colleagues in contemporary astrophysics and cosmology.

    A low third peak would have falsified LCDM. It survives that test. That does not automatically falisify MOND.

    Not that the statement is wrong! The statement is correct, and I do not dispute it as such. (Personally, I am interested in MOND and other modifications to GR in exactly the sense that Sean describes above). Rather, my objection is with the suggestion that the validation of a strong prediction of a theory like LCDM, as with the WMAP observations of the CMB, and potentially Planck observations to come (see Sean’s figure above), accomplishes no more than its “failed falsification”.

    This falls in line with a Popper-esque view of science as being all about falsification and failures of falsification – as if all theoretical predictions are equally valuable, and the victorious theory is never distinguished from the also-rans except by being the “last theory standing” once the appropriate suite of observations have been made. In addition to being inconsistent with the history of science as we know it (What exactly about Eddington’s eclipse expedition, and its falsification of Newtonian gravity as applied to photons, would lead to the almost immediate and universal triumph of GR, in Popper’s scenario?), it fails to comprehend the crucial role that Bayesian evidence can and must play in selecting the preferred model for explaining any particular phenomenon.

    I won’t review the underlying mathematics and statistical framework here. Suffice it to say, the Bayesian evidence allows us to quantify the *power* of a theoretical prediction, and as a trivial corollary, proves that not all predictions are created equal. Specifically – and coinciding with scientific intuition, including Occam’s famous razor – highly-constrained predictions that pick out a small portion of a much larger parameter space are much more valuable than weak predictions that accommodate a broad range of parameter values. Using Bayesian evidence, we can show that theories that pass a highly-constrained test in this sense are much more than “not falsified” – they have given us strong reason to prefer them to all alternative theories that either make weaker predictions, or worse, make none at all. Popper was wrong, in this sense – validation of theories is an important element of the scientific process, and not just because it falsifies theories that make contrary claims – the confirmation aspect is vital.

    Ignoring or minimizing the Bayesian evidence that has accumulated in favor of LCDM since MOND was first proposed decades ago, either by dismissing LCDM’s minimum necessary elements as mere “epicycles”, or by brushing off its successes, including the CMB power spectrum and the mass distribution of the Bullet Cluster (and others), is a dangerous game. In particular, it fails to “play fair” by conceding to the opposition its triumphs, and acknowledging the burden on all parties to identify the best, most highly-constrained tests that can be carried out going forward, in search of high-quality evidence for one model or the other.

    In the limiting case, the attitude that the burden is on the community at large to falsify your theory – with no corresponding acknowledged responsibility to propose and carry out uniquely validating tests that would strengthen the Bayesian evidence in your theory’s favor – is the common distinguishing characteristic of conspiracy theorists of all flavors. Avoiding even the faintest whiff of this attitude should be a high priority for theorists wishing to swim in the mainstream of their science. And yet this is the trap that I fear many MOND advocates are slipping into, more or less unawares.

    Which would be too bad, because as I think this dialogue (word applies to N>2 participants, by the way, no need for neologisms) shows, there are important LCDM critiques to be explored, including those motivated from a MOND perspective, and at a very basic level, there is surely no guarantee from the Universe that gravity is pure unmodified GR “all the way up”.


  7. Hey, I’m just a lowly wind-turbine engineer and certainly no specialist in this area, so I gave up reading about half way. However, the thing that seems obvious to me (and has probably been disproven by you experts for technical reasons) is that dark matter is just ordinary baryonic matter that’s in another brane from ours. The only thing that propagates between the branes is the gravitational fields, so we can only infer it gravitationally instead of see/feel/taste/touch it. I can envision galaxies in nearby branes that orbit(?) about galaxies in our brane and are closely aligned with ours. That added gravitational field might help “flatten the rotation curves.”

    I would think that a dense location in a brane in the early universe might help seed galaxies in that brane and other branes, thus making them somewhat aligned. There may also be galaxies in other branes that are not aligned with galaxies in our brane (but maybe with galaxies in other branes). This might appear as a dark-matter galaxy and would bend light around what appears to be nothing.

    I suppose I should give Lisa Randall credit for giving me this inspiration when I was reading her “Warped Passages” book. A figure in the book gave me the idea, although she never actually discussed the idea it gave me.

    Let me apologize in advance for throwing out something that has probably already been dismissed.

  8. Doesn’t anyone else find it sad that these particles for which nobody has any observational evidence have to be imbued with properties which no other known particles have to explain, e.g., cuspy halos?

    Why should MOND, which is non-falsifiable and violates the cosmological and Copernican principles, get more press than black holes? There have been dozens of intermediate mass black holes confirmed in the past few years, up from two known in 2008. Paul Frampton and his co-authors have repeatedly stated that there would be plenty of density in the early universe to explain black holes of about 100,000 stellar masses if inflation began slower than it ended — a question on which we have no information either way — without disturbing the baryon nucleosynthesis ratios. Such black holes, numbering about a million per galaxy, would not be sufficient to disturb strong lensing results or the CMB fluctuations in e.g. WMAP data. Microlensing studies have only ruled out point sources 10 stellar masses and below. The orbits of wide binary stars are compatible with 100,000 stellar mass black hole dark matter, too.

    Unless the rate of intermediate mass black hole discovery suddenly grinds to a halt, we will soon pass the threshold at which any particle dark matter, if it ever existed, will be known to have fallen in to black holes anyway. (“Primordial Black Holes as Dark Matter: Almost All or Almost Nothing” arXiv:1003.3466)

    Mark my words: The names of the cosmologists who neglected black holes will figure prominently when Congress votes to slash science funding, when school boards vote to give creationism equal time, when vaccination proponents go on the air, and when preachers lead their flock away from rationality, unless they straighten up, fly right, and stop giving lip service to the evidence-free unicorn cosmology of particle dark matter.

  9. Sean- Are you saying DM doesn’t collide with anything, including itself? If it’s in a separate brane from ours, it can’t collide with our own matter, only gravity can propagate between branes.

  10. Emails on dark matter. Better be careful someone might hack in and steal them. It’s a vast global conspiracy by scientists. They’ll be calling it dark matter-gate.

    It’s a great read, or at least I assume it is. After finals I’ll sit down and absorb it all!

  11. James:

    There have been dozens of intermediate mass black holes confirmed in the past few years.

    I don’t believe this. It’s true I work on SMBHs, but I’m interested in IMBHs and have colleagues who do work on them, and the last I heard is “we have some interesting candidates.” I haven’t heard of any confirmations actually accepted by the astronomical community.

    From your belligerent tone I’m guessing you’d agree with that last statement, but blame the community. While I could understand particle physicists ignoring IMBHs to focus on a new particle, what possible explanation could there be for astrophysicists to ignore this wealth of data you claim?

    An ADS search for “IMBH” turns up a lot of papers, of course, but they all seem to be about “candidates” or data “consistent with an IMBH”. A 2012 ApJ paper (Farrell et al.) refers to the “strongest candidate” IMBH. Not much you could call a “confirmation”.

  12. Marshall:

    Are you saying DM doesn’t collide with anything, including itself?

    Yes. Or, more precisely, it has a very small cross-section for self interaction, and we don’t know how small it is (I assume it’s still consistent with zero, or we’d have heard lots about that). This is what “collisionless” means when people talk about collisionless dark matter. (And why the dark matter and baryonic matter distributions are different in the Bullet Cluster.)

  13. James: confirmations, James, confirmations. See my edited post above about looking for recent IMBH papers on ADS.

    Your last paragraph was belligerent, or a poorly done joke. Sorry, it’s hard to tell online.

  14. That’s nice, Sean. Thanks for sharing with us this discussion.

    Could you share some thoughts on another alternative to dark matter, namely the running of Newton’s constant with the scale, for example in asymptotic safety scenarios?

    I’ll add here some references:


    or in Horava-Lifschitz gravity:

    Thank you

  15. I should add that IMBHs probably do exist. They seem like a reasonable way to get HLXs. We have to have them if SMBHs came from stellar-mass seeds. It’s just an overstatement to say we’ve confirmed any, let alone many, because it’s really hard to do.

    I also don’t see how IMBHs in a few globular clusters, etc., obviate the need for dark matter, but that’s a different discussion.

  16. Charon, here is the same search with the keyword “confirmed”.

    How would you raise the issue I am trying to raise without seeming belligerent?

    I recommend these peer reviewed papers on black hole dark matter, from the Journal of Cosmology and Astroparticle Physics and Astroparticle Physics.

    This one from the Monthly Notices of the Royal Astronomical Society argues for black holes which are so small they have been ruled out by microlensing studies, but the evidence shown against particle dark matter is interesting.

  17. James, a google link with a particular keyword is not evidence. You actually have look at the papers – least glance at the abstracts.

    Examples of how these papers actually use the word “confirmed”:
    “are not confirmed by our study”
    “if the luminosity can be confirmed”
    “it is essential that its association with the host galaxy is confirmed”
    “cluster presents a large-scale global rotation… confirmed with proper motions”
    “this result has not been confirmed”
    “inspection confirmed that there were very few stars that were missed by the automated routine”
    (these are all from just the first page of links)

    A google search for “sean carroll mates with turtles” returns over 100,000 hits. This is not evidence that he actually does.

  18. Oh, and avoiding phrases like “unicorn cosmology” when talking about the accepted scientific consensus would help with the apparent belligerence.

  19. Why doesn’t I hear more people talking about this paper:

    With standard GR, they explain how the quasi-isotropic structure of the clusters creates the rotation curves.
    It doesn’t replace dark matter completely, but it removes the need to explain rotation curves.

    There are also strong indicators that we are missing a lot of molecular H gas. Interstellar medium astrophysicists always use CO to trace H2 gas, but recently, HI self absorption seems to show that we are missing an awful lot of cold H2 gas.

  20. Charon, do you think there was a reason that I asked you for your count of confirmed IMBHs instead of a list of counter-examples from that search? For instance, is this an acceptable confirmation?

    How would you describe a theory which lacks empirical evidence and is more popular than an alternative supported by observations?

  21. Hi there,
    I wonder why in this discussion the growth rate of structures has not been considered. Accepting gravitational instability, if the universe had only baryons, and with the observed CMB anisotropies, perturbations would not grow enough from recombination to today to make galaxies. Dark matter provides the required significant boost. Is this so easily modeled by alternative gravity models?

  22. Hello. Wonderful discussion. I had to read it twice to understand the spotlights. Let me review some of them (and please, tell me If I am wrong with those):

    1. Non-baryonic darm matter exists.

    2. There are problems with the third low peak in the CMB spectrum. Likely, Planck will shed light on those issues raised by WMAP.

    3. The question is not really CDM versus MOND. The question to anwer and understand is what makes the universal rotation curve flat at large distances from the center while keeping the low distances almost-newtonian plus GR corrections.

    4. Non baryonic dark matter COULD be part of some kind of modified gravitational theory (MOND / or MOG are the current paradigms in modified gravity but there are not the unique nontrivial modification of gravity that theorists could imagine or invent). Then, MOND and CDM are perhaps part of the same puzzle, and they are not so different after all.

    5. Observations in clusters “prove” that some form of non-baryonic DM exists.

    6. There are solid evidence of a POSITIVELY accelerated Universe.

    7. From clusters we got enough evidende that there are forces pointing out to directions where there is “nothing” in the visible region.

    8. From WMAP and SUPERnovae we have evidence from some kind of “field” or stuff that behaves like a “cosmological (almost) constant” smashing apart different parts of the Universe as it expands.

    And now some of my own ideas about this intricate and hard problem. No quantum gravity theory has been built, and then I have never heard about the following option:

    -Dark Matter stuff and Dark Energy stuff are related with the old issue of a quantum gravitational theory.

    The sentence that it seems to be in the mind of Sean is “Nonbaryonic DM exists”. Is that opposite to some modified gravity? Not at all. Let me put this in a context. What about gravitons?(I will not speak of gravitinos in order to maintain my hypothesis apart from SUSY or any other local gauge theory modification for the moment). They are not in the SM of cosmology, we do NOT too much about gravitons (there is no quantum theory of gravity). So, they are dark. Mostly, the process graviton-> gamma gamma (for instance) must be likely suppressed by some king of symmetry (otherwise we could see graviton flashes in the sky).
    So gravitons are intrinsically dark (unless you build some modified gravitational theory with massive gravitons on which there have been some hard activity ultimately). Back to Dark Matter, one thing that I have ever been remarked is that of WIMPS. WIMPS have to interact very weakly with ordinary matter in order to meet the experimental bounds. I can not see any reason why gravity or some other companion quantum field could make the work.
    The most important unanswered question by both, MOND and CDM, is the rotation curve of galaxies, and if you want too, the distribution of DM in the galaxy to fit the models and/or the way in which MOND can obtain the galaxy profile, the CMB peaks and the observation on clusters. So, in conclusion:

    1. Four problems seems to be essential:

    -a) The flat rotation curves (with the fall at low distances to get Newton-GR at known distances where they works OK).
    -b) The low third peak in the CMB spectra posits problems for both theories (MOND and CDM).
    -c) Observations in clusters show that there are “something” else in the galaxies that is not light-emitting (or it does very very weakly, implicating some new approximated symmetry) but it interacts and feels gravity.
    -d) Dark energy seems to be the dominating the expansion of the Universe right now. LCMD supposes it to be a cosmological constant ( or something similar), something that acts like a harmonic oscillator in the Einstein’s equations F_Lambda=Lambda/6 R^2 ( R is the Scale factor). Harmonic oscillators are essential in quantum fields. But the cosmological constant oscillator has the “wrong sign” when compared with Quantum Fields (unless, if we considered a positive acceleration, like the observed one, as evidence for Lambda > 0).

    2. If DM particles do exist, they can be detected and likely produced in the laboratory. That is the hope of LHC Higgs-PostHiggs BSM theorists. Also, the wish of all the people working on direct/indirect DM detection experiments. ( Are the Fermi recent data around 130 GeV a hint. We will see).

    3. NO detection of DM particles in LHC or current DM detection experiments can shift the current preference on DM only to something more likely DM+Gravity modifications to GR.

    And I think, a crucial unmentioned question in this debate is the following:

    **** Can a modified theory of gravity EXPLAIN ALL the DATA WITHOUT THE ASUMPTION OF DM-LIKE HYPOTHESIS? I think, correct me if I am wrong Sean, that some of the CDM hotter defenders use to argue that MONDian physicists “at some point of their models” add some new field and then, at last, they are not making so different stuff after all. They are only shifting their assumptions. CDM theorists introduce some new field that enters the stress-energy tensor and modify gravity through it. MONDian theorists introduce some more general gravity theory that modifies the Einteins-Hilbert action. Moreover, it seems that Sean defendes that is more likely to add some field to the energy-momentum tensor than to change the effective action for gravity, but I am not sure of how much he agrees on that…I mean, Sean,

    a) Do cosmologists agree that we need extra components for the streess-energy-momentum tensor and they don’t come from ordinary fields we do know right now? I think the answer is YES.

    b) Do cosmologists agree that we need something like a cosmological constant to explain Supernova, Clusters, and other evidence for the current expansion rate of the Universe? I think the answer is YES too (Please, correct me if I am wrong).

    c) A more interesting question: why are cosmologists more afraid to consider non-homogeneous, or non-isotropic, or non-standard cosmologies that share most with MOND in order to bring out some effects we should explain from cosmological phenomenology than those based on the actual GR paradigm? For instance: CMB peaks (anisotropies of CMB), observation in clusters (couldn’t it be some complex dynamics of the gravitational field in collisions),

    A final question,

    What is the main problem to explain DM / DE with some unknown theory X that problably have effects on both the dynamical field equations in the matter-realm AND the geometrical side adding some exotic form of vacuum presion we “read” as an “almost” cosmological constant?

    I think MONDian physicists and CDM theorists agree in this point:

    GR is an effective theory. GR can not explain flat galactic rotation curves. Therefore, GR is a a low limit energy of some theory X. Mondians stress the fact that gravity will be modified, CDM people remark that new field enter into the game. It can be considered a complementary view. If you introduce a new field that couple to the universal gravity, you are modifying gravity (indirectly of course). If you introduce new fields sourcing the gravitational field ( a graviscalar, a gravivector, higher spin fields – forget about their problems to the whole discussion) then you have to explain how those new gravitational fields couple (nonuniversally or universally) to matter fields. Then, one could imagine some theory in which even new gravitational fields could be seen as some form exotic EM tensor plus a cosmological constant. Of course, one KEY issue is that cosmological constant is very tiny, so we get some hard bounds about how it can be done. CMB and MOND are not so different, … They are saying the same. And at last, I have no knowledge of any MONDIAN or CDM theory that explain the whole observations!

    I suppose MONDIANS and CDM-entities agree: there is no current theory that can take into account all the controversial data. They differ in how they face the same problems. But in the end, they are converging into the same puzzles. We need more data/more theory.

    Well, let me know what you think about my comments and remarks.

  23. James, my count is zero, and you’ve provided no evidence to the contrary. My point with those quotes was to demonstrate to you that you are not providing any evidence to the contrary.

    The Farrell et al. (2012, ApJ, 747, 13) paper I cited in my first post was on HLX-1. I’m going to trust a 2012 ApJ paper over a 2010 popular news site (that as far as I can see doesn’t even reference a paper). And “possibly confirmed” is pretty weak, especially given that it’s the headline of a pop news article.

    No one I know, including a number of people who work on IMBHs both from the theory and observation side, thinks IMBHs provide any significant contribution to dark matter. There is a fair amount of evidence for collisionless non-baryonic dark matter, which was Sean’s point for this entire post.

  24. Bepi, do you accept that black holes are at the center of most galaxies, including young galaxies? Consider the theories of supermassive black hole formation. Are there any which do not produce a larger population of intermediate mass black holes?

    Riemannium, what evidence do you think supports non-baryonic dark matter?

    Charon, are there any sources in support of your count of zero? Do you think it is reasonably consistent with the few years it took to confirm GCIRS 13E and M82 X-1?

  25. This discussion lacks the presence of non-cosmologists!
    You should try to find some more astrophysics/dynamics-related answer before jumping to new particles and new laws.
    Invisible matter? The only thing I think about is cold/inert HI gas. Hydrogen atoms are the most common things in the universe after all.
    Weird structures? What about turbulence? Intermittency in turbulence creates unknown fractal structures in space as well as in density and temperature.
    If I trust the mathematician/chaos theorist about the Far-field paper, rotation curves of galaxies are also explained!
    I don’t know enough about the third peak in the CMB though…

  26. James, have you read what I’ve written? Including the place where I said there were very likely IMBHs, in particular because “we have to have them if SMBHs came from stellar-mass seeds”?

    But, yes, of course there are theories of SMBH production that don’t involve IMBHs. Quasi-stars or direct collapse, e.g., Lodato & Natarajan (2006).

    You clearly don’t actually know anything about IMBH or SMBH literature, and given your refusal to use ADS and your willingness to link to pop news sites it’s now obvious to me that you’re not an astronomer. I started this conversation curious if there was some amazing new evidence for IMBHs that for some reason my colleagues hadn’t told me about, and while I learned a bit in my literature search, it’s clear I’m not going to learn anything from you. I’m done with this conversation.

  27. Charon, the Lodato & Natarajan (2006) paper you cite describes the production of 100,000 stellar mass black holes, in its abstract even. Where is the evidence that the process it describes results in more SMBHs than IMBHs?

    Do you believe that non-astronomers should be excluded from communication about these topics?

  28. OK lets try this again.

    I’ve never taken TeVeS/MOND too seriously for reasons already articulated by Sean. Nice discussion by the way – I like seeing that my arguments were never too far removed from what the paid professionals would articulate.



    No TeVeS in a binary pulsar system. No surprise but given the authors took the time to look I think it is worth noting.

    @ James Salsman :

    There is no observational evidence for your 100k M_sun black holes. Those beasties would majorly affect local stellar neighborhood dynamics, would accrete, and would be strongly visible via lensing.

    @ riemannium

    “-b) The low third peak in the CMB spectra posits problems for both theories (MOND and CDM).”

    Nope. Only MOND.

    Lamda-CDM explains the relative multipole peaks in the CMB quite fine and produce answers that are self consistent with other independent measurements of cosmological parameters.

    “2. If DM particles do exist, they can be detected and likely produced in the laboratory.”

    That is high order wishing and hoping.

    “**** Can a modified theory of gravity EXPLAIN ALL the DATA WITHOUT THE ASUMPTION OF DM-LIKE HYPOTHESIS? ”

    No. Stacy McGauch has even written papers on how the answer to that is “no”.

    “c) A more interesting question: why are cosmologists more afraid to consider non-homogeneous, or non-isotropic, or non-standard cosmologies that share most with MOND in order to bring out some effects we should explain from cosmological phenomenology than those based on the actual GR paradigm?”

    Because, by and large, the modifications do not work. It really is as simple as that.

    “GR is an effective theory. GR can not explain flat galactic rotation curves. Therefore, GR is a a low limit energy of some theory X.”

    No. GR accurately explains what is going on when you have something to shove into the right hand side of the field equations.

    It is widely assumed that GR is the low energy limit of some other as-of-yet unquantifiable theory of quantum gravitation but that distinction isn’t relevant for this type of discussion.

    “CMB and MOND are not so different”

    zuh? CMB –> CDM?

    Dark matter, believe it or not, is a pretty specific type of substance compared to something like MOND or TeVeS.

    Folks who advocate for TeVeS I think are somewhat missing the point when they argue a tensor field (10 components), vector field (4 components) and a scalar field (guess how many components) is a “better” alternative to dark matter.

  29. Eric, although there was a controversy about 10-5 years ago regarding wide binaries and other stellar dynamics, it was resolved such that IMBHs of about 100,000 stellar masses are consistent with observations on wide binaries as well as microlensing and considerations of disk stability. Please correct me if I’m wrong, but there are no lensing studies which have ruled out MACHOs above ten stellar masses. I certainly agree that they would accrete, but not long enough for the approximately one million which would be in the Milky Way to be producing apparent x-rays or UV more than a tiny fraction of the time. Again, if I have overlooked research on these subjects, please bring it to my attention.

  30. Fascinating discussion. Amusing parallel: there is no reason to believe our ability to weigh evidence works on very large or very small scales. Rainer recognises this. But how else could you proceed?

  31. Hi Sean, I always laugh how complicated some physicists make it for themselves. Most have gone WAY off track. I like your idea that dark mater is really dark energy that influences the effects of gravitation. This support Rangutan’s theory that gravitation is simply universal wind, radiation of sub-atomic particles, most likely R-bosons transmitted by black holes at more than the speed of light or even MORE likely that the constant in e=mc² applys only to our solar system and would prove that the constant is much LOWER towards the CENTER of the universe and explains the “dark energy” or missing energy or dark matter that confused scientists do not understand. RRG2012

  32. @eric Thank you for pointing out my two bigger errata:

    1) The third peak in the CMB spectrum is really no problem for LCDM. Yeah, but I think some mondian physicists are wondering on the systematics of that third peak. PLANCK will terminate the doubts some people has about it (although it is quite clear for some other people).

    2) The erratum CMB instead CDM. LOL…I was thinking in it obviously. I was thinking about CMB while I was comparing the two alternatives likely.

    I don’t agree with your view on GR. GR is an effective theory. It is not a quantum theory and it should somehow! Quantum theories are real ( and the quantum states are “real” in the sense we observe them). So gravity should also be a quantum theory. Otherwise, you should guess a classical theory reproducing the results of (quantum) local gauge theories.
    Eric, when you say:
    “GR accurately explains what is going on when you have something to shove into the right hand side of the field equations. ”
    Are you saying that GR CAN explain the rotational curves of galaxies?Obviously it does NOT! Are you saying that plugging the correct stress-energy momentum on the right hand of Einstein’s equations we should obtain that flat profile? I have not seen ANY paper on that issue! I mean, nobody has been able to guess the correct energy-momentum-stress tensor such as it produces v~constant. Obviously, if someone does it, he/she/they would explain the rotational curves and likely would receive the Nobel Prize. Anyway, if you know a reference on this topic (guessing the Tully-Fisher law or the flat profile from some concrete T_munu extra piece), please tell me the reference.

    Eric, notes that DM introduces extra fields in the matter sector. MOND introduces extra fields in the gravity itself. I was wondering that from that viewpoint, both theories “add extra stuff”. The essential point is that they differ in the key point of Dynamics and how interact with the other known fields. Of course, I am talking on a very general ground/setting.

    About the apparent absence of TeVes in a binary system. I would like to add that we should not expect to find it there. I think the MOND paradigm tries to be the game into de long IR of the gravitational theory. I should not expect TeVeS big corrections to binary systems, perhaps to Black Holes and with strong gravity but I have never expected MOND to be useful in binary stars (unless one of the objects be a BH candidate, something that should deserve a serious study, like CYGNUS X-1).

    I am well aware of the conceptual differences between MOND and Dark Matter theory, however, they show that we need some extra stuff in the SM and in Cosmology. We don’t have all the pieces to match the puzzle! And without the pieces (DM particles EVIDENCES greater than 5 sigma AND likely the Higgs particle stuff) we can not do much more excepting what Sean and others say.

    @James Salsman Personally, until we can see 5 sigma evidence of DM particles, I think is an hypothesis! However, as Sean and the other experts remark, there are compelling evidence of forces pointing to places where there is literally “nothing”. So, how could explain it? However, there are some recent papers claiming the contrary: that the hypothetical DM particles is not where it should or how it should be expected to be found.

    I am pleased to agree with you that in order to sustain the DM hypothesis we DO NEED to find them! Two scenarios:

    a) DM particles are found in the LHC and ony other direct/indirect experiment in the next decade. Boost of HEP and Astrophysics.

    b) NO DM particles are found in the LHC and other searches in the next decade.

    Well, in my opinion everyone is wishing and suspecting a) is the most likely scenario. The nightmare b) is yet “crazy” or “anatem”.
    And if I were pushed into what is the most striking hint of DM I would stress something that we do know is not completely as we had figured out in the SM: neutrinos. But that is another story…Since neutrinos, at least SM neutrinos we do know now, can not be the whole DM although perhaps they can be a part and “interacting”? part of them…Neutrinos pose other challenges but maybe they are also in this game…

    Cheers, and make more great posts! :D

  33. “Stacy, March 19: Science is dead.” Is Milgrom the Kepler of modern cosmology? Is J. Christian of Oxford the greatest theoretical physicist since A. Einstein? Is Pavel Kroupa one of the best astrophysicists in the world?
    I quote Prof. Dr. Pavel Kroupa from a (Nov. 1, 2011) e-mail,
    “My criticism is not based on me not liking dark matter, but is a result of rigorous hypothesis testing such that, from a strictly logical and scientific point of view, LCDM is definitely not a viable model of cosmological reality. I do not write such statements because I do not like LCDM and its ingredients, but because every test I have been involved with falsifies LCDM. At the same time, the tests of MOND we performed were done on the same footing as the LCDM tests. The MOND tests yield consistency so far. I am not more “fond” of MOND or any other alternative, but the scientific evidence and the logical conclusions cannot be avoided. And it is true, I must concede, that MOND has an inherent beauty which must be pointing at a deeper description of space time and possibly associated quantum mechanical effects which we do not yet understand (compare with Kepler laws and the later Newtonian dynamics).”

  34. Goodness!

    The philosophy of science matters deeply here. One aspect of that is objectivity. One way we’re suppose to remain objective is through a priori predictions. I “grew up” with dark matter and remain more comfortable with it than with MOND. But it was MOND that predicted what I observed in low surface brightness galaxies, not CDM. Reporting that was simply a matter of intellectual honesty.

    I’m happy to be persuaded I’m wrong. It would, in fact, be a great relief! I don’t like having these arguments. Indeed, I find it exceedingly unpleasant – hence my exasperation with our trialogue, wherein days and weeks of painful correspondence barely sufficed to bring Sean up to speed.

    An important but necessary detail to convince me that MOND is wrong is that the evidence has to suppose that contention. Having just written an invited review on the subject (http://arxiv.org/abs/1112.3960), it simply isn’t that obvious. I could have written a comparably comprehensive review on dark matter, both pro and con. I don’t think that any of the scientists who are most critical of MOND could do the same: most of them have never given it a chance.

    I feel comfortable saying that because I admit to having been the same way. MOND was obviously wrong and not worth considering. It required the direct shock of having it crop up in my own work to make me reconsider. My sin seems to have been taking successful predictions seriously rather than falling prey to the temptation of cognitive dissonance: to simply reject the evidence that didn’t fit with my pre-existing world view. Certainly that would have been easier, and better for my career. But if we do that, why bother doing science at all?

    Two things need to happen to persuade me that CDM is correct:
    (i) explain the observed phenomenology in galaxies, and
    (ii) detect dark matter particles in the laboratory.
    Until (ii) is accomplished to the mutual satisfaction of the many experimental groups that are competing for the inevitably resulting Nobel prize, how can we be sure we haven’t invented a modern form of ether? A ubiquitous, invisible substance that, given our current theoretical understanding, simply must exist. But does it?
    I honestly hope that the various direct detection experiments find a positive detection soon. Then we know. If they don’t, we don’t. So far, WIMPs have yet to be seen by direct detection experiments like XENON100 and CDMS, and there is no hint of them in indirect data like the gamma-rays detected by Fermi. These experiments have excluded vast swaths of the available parameter space. If the Higgs mass is really ~125 GeV, then colliders should already have provided evidence for them. That gives me serious pause.

    Does that falsify dark matter? Of course not. Perhaps, if additional searches fail, in the next few years we might decide that WIMPs haven’t panned out. What then? We make up something else. Axions would appear to be next in line. If those are confirmed, great. But if not? Do we abandon the whole paradigm? Or do we just make up some new, still harder to detect dark matter candidate?

    That is a profound worry from the perspective of the philosophy of science. While individual dark matter candidates are falsifiable, the concept of dark matter is not. I understand the reluctance to consider crazy sounding alternatives like MOND until all other possibilities are exhausted. But all dark matter possibilities can never be exhausted.

    If there is a persuasive laboratory detection of dark matter, then I will be willing to agree that the observed galaxy phenomenology [(i) above] must inevitably be explicable with dark matter. That is very hard. I frequently hear the complaint “MOND only fits rotation curves and nothing else.” People who say that need to read the review article. But lets just think about that one observation.

    The rotation curves of galaxies are entirely predictable from the observed distribution of baryons. That is a strong statement, and a test that MOND could easily fail. It passes. That surprises me. But what surprises me more is the contortions we have to go through to explain this in the conventional dark matter context. Dark matter dominates the dynamics, yet all we need to predict the dynamics is the visible matter. Why? It is like asserting that the solar system operates on an inverse cube force law. It just looks like an inverse square law because dark matter is arranged just so.

    I am repeatedly disappointed that the physical intuition of so many of my colleagues has atrophied to the point that they don’t immediately see the importance of this observation, irrespective of its ultimate interpretation.

  35. Hi Sean,

    Have you, or any readers/commenters, seen Colin Rourke’s current work which attempts to answer questions such as Rainer’s –

    “Crucial questions are: what flattens the rotation curves in galaxies? What creates the third CMB peak? CDM, MOND or something else?”

    as well as an alternative for the apparent red shift evidence for Hubble expansion among others, without *any* new physics? Here is the address for a paper in which he summarises all aspects of his work which also has links to his more detailed papers:-


    Would love to know what you make of his ideas!

  36. Dark matter vs. modified gravity + modified source of CMBR + modified velocity of propagation of transmission of data *).

    *) Einstein: “A curvature of rays of light can only take place when the velocity of propagation of light varies with position”.

  37. Nice to see Stacy is reading the comments here. I have a comment about this:

    “I correctly predicted the amplitude of the second peak (a prediction that is still quantitatively correct) by making the ansatz that there was whatever generally covariant theory might grow out of MOND looked just like GR in the early universe. Obviously that has to change later in order to grow structure, but at least it gives some proxy for what MOND might do with the CMB.”

    I remember the verification of this prediction. However, there is a set of cosmological parameters which fit all the data, including the CMB. At the time of the prediction, they weren’t that well constrained, but of course the present values are within the errors of the parameters back then. The non-MOND “model du jour” fit the data less well than the “MOND-proxy” model. However, that is more or less an accident of history. The non-MOND model could have been closer to the current best-fit parameters. Thus, I tend to see this verification of a “MOND prediction” as more or less a stroke of luck, and indeed as you say when the CMB data became more precise it was ruled out. I thus think it is a bit exaggerated to continue to tout this as a “MOND success”. I’m sure there are other examples where someone was “right” for the wrong reasons.

    In general, I think MOND people know more about CDM than vice versa (though this might be the only possibility for a minority to survive), and the one bona fide MOND person I know well personally, Bob Sanders, certainly has a good understanding of astrophysics and cosmology in general. However, I think both sides are guilty of over-confidence, e.g. Kroupa’s latest claims (see the discussion at http://telescoper.wordpress.com/2012/05/04/milky-way-satellites-and-dark-matter/ ) on the MOND side and, as you point out, unfair comparisons on the traditional side (e.g. comparing an ugly MOND+ theory to an incomplete standard theory).

    Although it is qualitatively not the same, since it was concerned with parameters within a theory rather than with a rival theory, folks should remember how strongly “the establishment” (meaning folks who control funding and in some cases ridicule those who think differently, well documented by eyewitnesses and even the New York Times) believed in Omega=1 and/or lambda=0 not that many years ago. Those who were open-minded and/or thought that a better model was a better fit to the data in some cases had a worse time than proponents of MOND today. Of course, that doesn’t mean that every maverick will turn out to be right (the fact that the mavericks don’t agree makes this impossible), but I think that both sides should invest a bit more time and effort in evaluating the other side objectively.

  38. Sean, can I ask how likely you believe it that WIMPs will be found in the lab? Stacy thinks they already should have been suggested. If WIMPs aren’t found, what then?

  39. It is important to remember that the motivation for cosmological dark matter comes from astronomy, astrophysics and cosmology. There is no firm prediction from particle physics. Dark matter doesn’t have to be some sort of WIMP. However, other candidates such as primordial black holes have been ruled out by observations, so there is not much left.

    Should one find them in the lab? It depends on what they are, how they are distributed, how easy it is to detect them etc. It took decades after they were postulated until neutrinos were detected, even though we knew their properties well and had a huge supply of them. If WIMPs are dark matter, they are much less numerous than neutrinos and we don’t (yes) know what their properties are.

    It is important to keep these two things distinct.

  40. I do not usually comment on such blogs, but since Stacy is active here I thought I might mention the following (notation: C/WDM = cold/warm dark matter, i.e. dark matter which is dynamically relevant on the scales of galaxies):

    In about 1997 I heard a brilliant presentation by Stacy McGaugh at Harvard about his PhD research. I remember that he began by stating that his original aim had been to falsify MOND using disk galaxies. Instead, he apologised many times to the audience (according to my memory) that he could not falsify MOND and that instead every prediction made by MOND was verified. At that time I had found solutions to the Milky Way satellite galaxies without dark matter (http://adsabs.harvard.edu/abs/1997NewA….2..139K ) but in Newtonian dynamics. All my computational work was done assuming C/WDM exists within the Milky Way, as predicted by the standard model, but my results were disquietening as they suggested that there is something not quite right with the statements made by every colleague I met. In a train ride from Switzerland to Germany a well established colleague told me (a postdoc then) off for having written this paper with the title “Dwarf spheroidal galaxies without dark matter”, as it was going massively against the generally accepted thinking (a few years later I was even told by a very high-ranking professor that I had become essentially unhirable because of that paper).

    And then I heard this talk by Stacy and realised that MOND trivially accounts for all rotation curves. My subsequent work (together with people like Manuel Metz, Marcel Pawlowski and others) turned out to be remarkably consistent with my previous results, and with those of Stacy by trivial implication, and the newest data are so completely in contradiction with the expectations from C/WDM models on scales of 10-300 kpc that one would need to be a non-scientist to still doubt the implications (http://adsabs.harvard.edu/doi/10.1111/j.1365-2966.2012.20937.x ; http://adsabs.harvard.edu/abs/2012arXiv1204.6039P ).

    The work by Mike Disney on disk galaxies, which are the by far dominant galaxy population in the universe, again shows the C/WDM models to not work – these galaxies are all too similar in conflict with the variation expected if C/WDM rules structure formation, and this is in turn also shown by too few disk galaxies having bulges. The recent attempts to form such observed disk galaxies within the C/WDM model fail.

    So either one modifies the C/WDM particle physics in the dark sector, i.e. one postulates/speculates that the particles interact in ways we do not yet know (how many additional degrees of freedom would this bring into the resultant model?, and would it then still have any predictive power?), or one reconsiders the foundations of the model. A review of all of this plus much more including discussions of the large-scale structure and the CMB evidence has appeared, and is likely to be greeted with some maliciousness, given the experience: http://adsabs.harvard.edu/abs/2012arXiv1204.2546K (I will be replacing it soon with updated and additional references and minor modifications).

    Concerning the blog by Peter Cole mentioned above by Phillip Helbig (#42), I am misquoted there: My statement was that dynamically relevant dark matter in galaxies cannot exist. Hot dark matter (within the framework of the Angus cosmological model which is based on Milgromian dynamics) is so far not excluded.

    A final note: everyone is free to make their own deductions given the data, but _if_ dynamically relevant C/WDM does not exist, then the claimed excellent agreement of large-scale structure observations with the standard model of cosmology becomes completely irrelevant because crucial physical and mathematical foundations of this very model would not be true any longer.

  41. Surely the basic problem here is that Stacy believes ‘galaxies are simple’ – and therefore should be somehow the prime data set for evaluating theories – whereas Sean believes that galaxies are complicated and prone to many uncontrolled uncertainties (baryonic physics, ‘feedback’ etc.), and that, on the contrary, CMB, large scale structure, and large galaxy clusters are simple, and should therefore be the prime data set.

    I think it is incontestable that the larger scales you probe in the Universe, the more you are dominated by gravitational interactions as compared to electromagnetic (i.e. stellar / plasma physics) and the more linear and simple things become. On this very basic observation one ought to prefer ‘large-scale’ evidence over ‘small-scale’ since in general small-scale phenomena are more non-linear and have more complexity and are more strongly influenced by non-gravitational interactions.

    But then Stacy counters that modelling baryonic physics within galaxies constitutes a whole new lot of adjustable parameters which can be massaged to fit any data we want… which somehow counts against the CDM side, while leaving MOND untouched. So galactic physics ought, morally, to be simple, and we ought not to try and make out that it’s complicated? Well, where is the demonstration that galactic physics is indeed simple? Where is the simple, explanatory theory of how galaxies formed and what happens inside them?

    Regardless of your theory of gravity and regardless of the presence or absence of dark matter, the physics of baryonic matter in galaxies *is* often complicated, *does* have to be modelled, and such models are observationally testable – precisely by observing galaxies. Epicycles are not in themselves observable, but galactic feedback ought to be.

    For the argument that ‘galaxies are simple’ to stand up, one ought to be able to describe how they formed, and why they now look like they do. As far as I can tell MOND proponents don’t do this: they point to many observational regularities that existing galaxies seem to obey, and then leap to the conclusion that since MOND, applied to a static and ready-formed population of galaxies, fits these regularities, it must beat any other theory in which galaxy formation is a complicated and not completely modelled process: since such theories “cannot possibly” reproduce the observational relations.

    This is not a fair comparison of like with like. If you want to test theories by their predictions about galactic properties, either you calculate galaxy formation in both using comparable methods, or you admit that you are asking one theory to do a significantly different job from the other. The remark ‘MOND predicts X whereas CDM predicts Y’ is misleading if the word ‘predicts’ has very different meanings for the two models.

  42. @45: Thanks for contributing. You write above:

    “Concerning the blog by Peter Cole[s] mentioned above by Phillip Helbig (#42), I am misquoted there: My statement was that dynamically relevant dark matter in galaxies cannot exist. “



    one can read:

    Kroupa concludes by highlighting the wider significance of the new work. “Our model appears to rule out the presence of dark matter in the universe, threatening a central pillar of current cosmological theory. We see this as the beginning of a paradigm shift, one that will ultimately lead us to a new understanding of the universe we inhabit.”

    That is a direct quote. If you didn’t say or write that, then you should ask them to correct it. Being misquoted can ruin one’s reputation. :-)

  43. [I’m a layman and not understanding most of the details here.] The argument that CDM implies two types of dwarf galaxy and the type we can see already have sufficient mass to account for what we experience (is that right?) sounds like an attempt to be logically decisive, rather than just aggregating evidence. What’s the problem with it?

  44. @stringph: We violently agree.

    X and Y are indeed not comparing apples with apples. That is what makes this whole business so hard.

    When I say galaxies are simple, I mean that one can write a single equation that connects the observed dynamics to the observed mass distribution. That is an empirical statement. It happens that the equation is that of MOND.

    In LCDM, we need to understand galaxy formation, feedback, etc. as you say. I have struggled very very very very hard to understand how one simple equation falls out of that. All I can tell you so far is what doesn’t work: it is a very very very very very hard problem. Whether it is impossible is impossible to say. But neither it is obvious that it is possible, let alone inevitable as many people seem to assume. [LCDM is obviously right, so surely it will work out…]

    We do not need to understand how galaxies form in MOND in order to test it any more than we need to understand how the solar system formed in order to test Newton and Einstein. This is one of the painful ways in which the theories differ: apples and oranges. Which is better seems to come down to which fruit you like better (or are more familiar with).

    There are many many modified gravity theories that obviously do not work. Once you write down a force law, you are stuck with it. So it is amazing that MOND works as well as it does – it could, and should fail in lots of places where it works quite well. I want to understand why that is. At the very least, it is telling us something remarkable about galaxy formation in LCDM. Perhaps it is telling us something even more profound.

    I have yet to hear a persuasive argument why MOND works even a little bit. Mostly what I hear are assertions that it can’t possible be true. I understand that – better than anyone. That’s what makes it important.

    FYI, some time ago I put together a table of where LCDM and MOND work and don’t work. It really is orthogonal – apples and oranges. So it still boils down to which fruit you pick: http://www.astro.umd.edu/~ssm/mond/LCDMmondtesttable.html

  45. Julianne Delcanton’s point seems to have gotten lost in the noise, so let me say that I think it is the thing that should be addressed most carefully:

    The much-celebrated decent fits to a single parameter seen in MOND papers deserve explanation. Whether that explanation involves modified gravity, a new empirical rule found from structure simulations, some sort of (g)astrophysical understanding of galaxy formation, or something to do with solving galactic disk formation is the real open question. All these hypotheses have been placed on the table, but there clearly are problems with taking the “MOND-only” approach that seems to be the bread-and-butter of many of the Milgrom-boosting camp (Disney, Kroupa, McGaugh, and others). The issue of “dark matter”, though informed historically by rotations curves, shows up in so many other places in cosmology and astrophysics that it is irresponsible to claim that galaxies alone push away the WIMP hypothesis and demand a scientific revolution in cosmology.

    Or maybe I misinterpret that camp’s perspective.

    What I would like to see is a bit less sound and fury about falsifying Lambda-CDM coming from the MOND-boosters and a little more work on what the special acceleration/gravitational potential could mean in terms of detailed look into the state-of-the-art cosmological/galaxy formation theory and observations. That’s why I think Julianne is right on the money here.

  46. I don’t agree with Derek Fox (comment 7) that Popper’s approach is wrong. Popper described the essence, and later others extended the picture. If a theory is verified, especially when it made a highly-constrained prediction, then that gives confidence in that theory. But only until the theory fails a test. It can have had many spectacular successes, they don’t help if it one day gets proven wrong. The support a theory gets by passing a particular test is more a psychological effect, and not a strict logical one. We might prefer the theory because of that success, but this does not prove it to be right, or ‘more right’ than *every* possible (maybe not even imagined) alternative.

    When Derek writes “avoiding even the faintest whiff of this attitude should be a high priority for theorists wishing to swim in the mainstream of their science“, I agree with him that one needs to try to falsify one’s theory. But this statement has an implication which he might not have intended. Why at all should it be desirable for a theorist to ‘swim in the mainstream of their science’? This might be interpreted as an ‘either you are with us or you are with the crackpots’ kind of argument. I don’t think it would be science anymore if we aim at agreeing about everything right from the start of the development of a new theory. Yet I see a similar kind of attitude expressed by some colleagues (certainly not in the majority). Do you think it is good scientific practice for a professor to tell a student that he ‘would never hire anybody who has written a paper on MOND’? I don’t think so, but heard exactly this once, as well as many warnings that criticizing the mainstream theory puts your career at a severe risk. Is this still a good advice or is it intimidation? To be honest, when advocates of a theory use such means, I am growing suspicious of their motivations. A good-standing theory should not need this kind of behavior. If you are convinced that the theory you favor is the correct one, there is no need to be afraid of alternative approaches, as you can be confident that they will turn out to be worse than your theory.

    As said, Popper’s description was not the final one, there have been several important modifications. Falsification is not as simple as one might imagine, one has to be sure that the falsification itself is a certain one. Scientists seem to prefer to modify favorite theories instead of rejecting them, or they, as Imre Lakatos described, even add a protective belt of auxiliary hypotheses to make sure the theory survives observed anomalies. In addition, if there is no alternative theory readily available, scientists seem to prefer to work with a theory which has been falsified. It is better than nothing, after all. Now this shows why it might become dangerous to discourage research in alternative directions: we might get stuck with a theory having many problems, but the mainstream not willing to give it up because no equally developed alternative is available. In my opinion, we should not discourage non-mainstream ideas, but encourage them. We should avoid focusing all our scientific attention on just one theory. Researching and listening to alternative approaches is important.

    Coming back to the question of cold dark matter and Josh’s comment (53): one should look at the broader picture, yes. Currently, more and more cracks open in the standard cold dark matter theory (CDM). In the past few weeks alone there was the Moni-Bidin et al. paper, our work and also a paper by Karachentsev, showing that there is also a factor of 3-4 less dark matter in the local universe than predicted by cosmology. And there are many more known problems without solutions (see the list in Pavel’s paper, for example). The rejection of an alternative theory like MOND does not make the mainstream theory’s problems go away. Pointing out that one theory fails does not put you into the ‘boosting camp’ of a particular alternative. People do not search for dark-matter problems to promote MOND. The problems motivate why alternatives such as MOND are worth looking at.
    It might well be that we are witnessing the early stages of what the philosopher Thomas Kuhn described as a scientific revolution. The current situation certainly resembles the structure of science as described by him. Most of the time, we do “normal science”, working in an established paradigm (CDM in this case). But as more and more problems add up, science reaches a crisis from which a new paradigm emerges. It is already becoming more fashionable to at least modify the theory, some cosmologists switch from cold to warm dark matter, for example. We might therefore be approaching this last phase, where new ideas can lead to a jump in understanding. If that is the case, the next years will become very exciting.

  47. Do we really know what gravity is, other than GR models it as warped spacetime? When mass turns to energy, it expands greatly. What happens when energy turns to mass? Would there be a corresponding contraction and gravity is not so much an effect of the existence of mass, but the creation of it?
    “According to Porter, the new analysis leads to several conclusions. For example, it shows that the density of cosmic rays is higher than anticipated in the outer regions of the galaxy and beyond the central galactic plane. In addition, the total amount of gamma radiation from cosmic ray electrons due to interactions with infrared and visible light – which consist of photons of much lower energy than gamma rays – is larger than previously thought.”
    So the missing mass can’t be found, but there is a halo of excess cosmic radiation. So starting on the perimeter of galaxies, down to the core of massive bodies, there is a constant collapse/fusion of energy into ever more dense mass. Wouldn’t this contraction create a corresponding vacuum effect?
    That way, the mass being formed is equivalent to the vacuum effect pulling it together, creating the flat rotational curve of galaxies, as the process is uniform.

  48. Phillip, it’s not really accurate to say that black holes have been ruled out by observation. They have fallen out of favor mainly because most cosmologists don’t realize that the baryon nucleosynthesis ratios depend on density during early inflation, and we have no information about whether inflation expanded at a constant rate or whether it started slower that it ended, in which case there would be sufficient density for primordial IMBHs.

    Someone please correct me if I’m mistaken, but I don’t think there is a single observation inconsistent with the 100,000 stellar mass black holes which Frampton has been publishing about for about a decade.

  49. Why do you feel that (weak,strong) lensing does not falsify the notion that there is a large amount of IMBH’s scattered in the galaxy?

    Remember what the lensing surveys look for : transit events. Why do you think the black holes are immune to that?

  50. Eric,

    Massey, Kitching, and Richard (2010) say:

    “There have been extensive and sustained efforts to characterise the number of MACHOs in the halo of the Milky Way, its satellites the Large and Small Magellanic Clouds, and our neighbouring galaxy Andromeda (M31). Even though MACHOs are not visible themselves, whenever one passes in front of a star its gravitational microlensing briefly brightens the star. Since the volume of space along lines of sight that would cause microlensing is tiny, many millions of stars need to be continually monitored. Looking towards 12 million stars in the Magellanic Clouds for 5.7 years, the MACHO survey [306] found only 13–17 microlensing events (and some of these have been challenged as supernovae or variable stars). At 95% confidence, this rules out a model in which all of the Milky Way’s dark matter halo is (uniformly distributed) MACHOs. However, if all events are real, the rate is still ∼ 3 times larger than that expected from a purely stellar population, indicating either that they contribute up to 20% of the Milky Way halo’s mass [307], or a larger fraction of the Magellanic Cloud halo, in less massive bodies [308]. Also looking towards the Magellanic Clouds, the Experience pour la Recherche d’Objets Sombres (EROS) project [309] found only 1 event in 6.7 years of monitoring 7 million stars, compared to the 39 expected were local dark matter composed entirely of 0.6E−7 – 15 M⊙ MACHOs. Looking towards the Magellanic Clouds and the densely populated central bulge of the Milky Way, the Optical Gravitational Lensing Experiment (OGLE) [310, 311, 312] detected only 2 microlensing events in 16 years, and even these events are consistent with self-lensing by stars, rather than MACHOs [313, 310]. The OGLE results conclude that at most 19% of the mass of the Milky Way halo is in objects of more than 0.4 M⊙, and that at most 10% is in objects of 0.01–0.2 M⊙. The POINT-AGAPE experiment [314, 47] observed unresolved (pixel) microlensing in the more distant Andromeda galaxy, and found that at most 20% of its dark matter halo is in 0.5–1.0 M⊙ mass objects (at 95% confidence).”

    So that rules out uniformly distributed MACHOs and MACHOs less than 15 M⊙, correct? Frampton’s distribution of black hole dark matter around 1E+5 M⊙ doesn’t even come close to being excluded.

    What other lensing results impose constraints?

    P.S. Sean, would you please ask your sysadmins to allow <sup> and <sub> tags in comments for super- and sub-scripts?

  51. NASA’s IBEX has established the speed of the Solar System at 83.000 km/hour, 11.000 km/hour (about 12%) slower than thought before.

  52. I think that to really rule out a theory, you are going to generally need some sort of laboratory test; in tests of gravitation, the “laboratory” is the Solar System. Can MOND/TeVeS be tested in the Solar System ? It turns out it can, in the special locations where local gravitational accelerations cancel. There is a serious proposal to do this with the LISA Pathfinder, after its primary mission, by using a WSB trajectory to get it from the Earth Sun L1 Lagrange point to where the Earth/Moon/Sun gravity all cancel. The LISA/Pathfinder accelerometers (being used as a gradiometer in this case) should have more than enough sensitivity to either confirm TeVeS, or push it into a very uncomfortable corner of its parameter space, and this test should be doable in this decade.

    Basic references :


  53. eric gisse @57 : While the optical depth of being lensed is independent of the mass of the lenses in a MACHO scenario, the duration is not. If the typical lens mass is much less than the Earth’s, the events are typically hours or less, too quick to reliably see (at least, without some Kepler-type space mission), and if it is bigger than ~10^4 Solar masses, the events take longer than we’ve been observing for them (decades or longer). So, microlensing only really constrains MACHOs between those two sizes (and, the actual upper limit is less than 10^4 for existing surveys). See Equation 44 here for the math :


  54. @56 und 62: Microlensing surveys place tight constraints on the amount of dark matter in compact objects. Primordial black holes are independent of nucleosynthesis, so that is not why they are ruled out. Very massive black holes would also be visible: not necessarily in microlensing surveys, but because of other types of gravitational-lens effects.

  55. By the way, I (the Marshall of # 61 and 62) am not the Marshall of # 8 and #12. I wasn’t aware this didn’t force name uniqueness, so I will expand my name.

  56. On http://arxiv.org/abs/1205.1450 . This constrains TeVeS and a set of similar theories, but does not rule it (or them) out.

    To quote from the paper :

    “Therefore, the results of the present paper do not rule out TeVeS, but show that its original 2004 formulation by Bekenstein may need to be amended. At present, even its original writing is consistent, although it does need some tuning.”

    (I assume that by “original writing” they mean “original version,” but at any rate this does not seem conclusive, one way or the other.)

  57. great success! my technical reply is being marked as spam. now to figure out why…

    FUCK. This commenting system ate yet another technical reply and I’m sick and goddamn tired of retyping. Forgot to copy before submitting and poooof! Not sure why WordPress is being such an asshole to me but, hey, WordPress.

    I think this is the 5th time on a second day I’ve tried to submit this:


    OGLE I-III, with IV in progress, EROS I and II, MOA, SuperMACHO are examples of microlensing surveys.

    The basic problem with black holes as IMBH’s is that it doesn’t make too much sense WRT galactic formation given the fact that galaxies only have one central black hole unless there’s been a merger. Its’ my opinion that black holes were the nuclei that galaxies formed around but that is a bit speculative…

    @ Marshall Eubanks:

    That particular paragraph isn’t a surprise to me. They’ll just try another form with maybe a few more free parameters all the while arguing it is a serious theory.

    That paper really does rule out TeVeS given it nulls out a crucial parameter within the theory tha would distinguish it from other relativistic theories like GR. If they want to play the game of shifting the goalpost then they can go right the hell ahead but they’ll pay for it with zero traction within the community at large.

  58. OK so the OGLE link is being treated as spam. WordPress is stupid. Nice to know why my comments were being silently dropped…

    The OGLE link I wanted to share: http://tinyurl.com/bqnofhz

    Also @marshall 62, the scaling goes as the square root of the lensing mass. Crossing times are still short for an IMBH even at human scales. The variously above-mentioned surveys have something like 20 years of integrated telescope time put together and if nothing has been found then I personally find it quite hard to believe that a large volume of IMBH’s is an acceptable alternative even without taking into account the various dynamic and optical (from accretion) issues they would generate.

  59. Phillip Helbig @62 – I actually looked into this around the time the ICRF was being set up.

    Suppose you want to constrain black holes with a mass of 1 million Solar masses. You would need about 1 million of these to make up the Galaxy’s missing mass. Suppose they are spread around uniformly out to 100,000 light years, then the mean separation is order 1000 light years, so there might be one about 1000 light years from us. At that distance, the angular size of the Einstein radius is about 3.6 arc sec. With 1000 VLBI sources, the nearest is likely to be about 3.6 degrees away. The deflection at 2.6 deg is 2 mas, easy for VLBI _if you knew where the source was without lensing. Alas, you don’t, and the trouble is that the proper motion is only 0.02 micro as / year, well beyond the ability of current and any likely VLBI. Gaia will have a much higher source density, but of sources with their own proper motions, which will obscure the lensing from IMBH.

    So, I don’t think you can rule out IMBH, at least from astrometry.

  60. Phillip Helbig @ 68 – I’ve red The Paper and found it thoroughly entertaining. It would be appreciated if you could point to “papers” of this kind more often – how do you find them?

  61. By the way, I think that if there were anything like 1 million IMBH in the galaxy, we would observe them directly. I don’t think 1 million “milli-quasars” would be easily missed.

  62. Eric, are there any theories of SMBH formation which do not predict a vastly larger number of IMBHs? Charon suggested Lodato & Natarajan (2006) above, but it actually predicts the formation of median 100,000 stellar mass black holes, exactly in line with Frampton’s papers.

    Marshall, how long does it take for an IMBH to clear its accretion disk? I’ve read that they can swallow a solar mass in years, not decades, and how often would that kind of an encounter occur? I think most of the million IMBHs would likely be visible for much less than a millionth of the time. Is there any peer reviewed work on this?

  63. I don’t know the SMBH formation theories that well, so I’m just going off my personal intuition and the lack of commensurate evidence.

    re: eating time, since we don’t have direct observations of an IMBH, we don’t really know. Besides, it is hard to quantify ‘how long’ because that would depend on how the star got too close. Eg, was it a grazing pass that’s now destroying it or a near-on hit?

    I think stellar devouring is less important, observation-wise, than orbital dynamics and accretion of nebulae and background dust which would add a nice localizable noise source in the sky. This times the tens of millions of them that would be needed to fill out an average galaxy’s halo means that odds are one of them would carve a path through a stellar nursey and leave a nice wave as it travels.

    Plus there’s the fact that one of those would be a huge gobular cluster unto itself in terms of sheer mass. That would have to make a mess of local orbital dynamics.

  64. Eric, I believe that most of the IMBH candidates in the Milky Way are associated with globular clusters, although there was recently at least one such cluster where an IMBH was ruled out. I wish we had more information about the expected lifetimes of accretion disks from both interstellar media and stars. For a galaxy the size of the Milky Way, you would expect only about a million 100,000 stellar mass black holes if they comprised all dark matter, not tens of millions.

  65. Mass-time gravity constants in propulsion mechanics may indicate a new area in contemporary physics.
    Through contemporary physics, an ethical foundation exists by popular belief, around the physics of light. Dark matter singularity initiates a process around solid states and their contemporary physics, where contemporary ethics fills a void in the gravity and their determinable quanta. To produce solid state physics, the research was aimed at high gravity of relativity. Most projections do not state that the reaction of conservation mass in an applicable quanta, are set as provisional rule, setting the relativity. Quantum relativity as ethical divide of the states in matter, bring fermions into question through their induced force fields and super relativity. The super relativity field initiates neutrinos as a quantum velocity and is applicable to tensor mechanics through its field frequency. As a subset, the field frequency applicable should correspond to magnetic inferences from gravity, and thus a polar bond is formed to demonstrate cohesion through magnetic field frequency. To respond to gravitational pull, the deterministic zero in magnetic constants should initiate correspondence through frequency resonance, through unified field theory. The initial results will produce dark matter relativity as the subject of neutrinos. The theory of condensed matter and gravitational pull exhibits dark matter relativity as a state of fermions in interactive shells, as a dual fractal hypothesis of conservation mechanics in dual tensors. The double spin theory with fermions interactive at the sub class domain, introduces the state of fermionic reactions, as an independent study of class fermions with perpendicular spin to the event horizon. A new relativity theory begins to emerge as the combined effects of general relativity initiated by a tensor spin. Activation of propulsion by a relativity wave sets the nuance for a new indicator of theory as the mass-time movement of natural relativity.

  66. Well, it would help to define the anagrams. MOND – I’ve encountered this before – Modified Newtonian Dynamics or somethin’ similar. But then right away I come to CDM – Somethin Dark Matter, then LCDM and CMB. I give up.

  67. @77: Cold Dark Matter, Lambda Cold Dark Matter, Cosmic Microwave Background.

    @70: I think this one was from the blog of John Baez, former proto-blogger and now real blogger at Azimuth, whose cousin I will see on 3 June. It was either mentioned in a comment or a link from a comment led to it (after not too many intermediate steps).

    The interesting thing about the web is that one can link to this stuff. I have an interesting collection at home (including self-published hardback books) which are just as good but not available to the general public. :-)

  68. Why did Stacy finish with “science is dead”? The only thing I know is that MOND is dead, but MOND is not really science, or at least not good science. So why does this mean that science is dead? What is going on here?

  69. Riemannium, I think that paper tries to solve a problem that doesn’t exist. Galaxies, stars, and black holes all form galactic/ecliptic/accretion disks. Trying to explain them with special pleading at a particular scale goes against the cosmological principle.

  70. A few supplemental points:

    1. Considerable evidence falsifies the cold dark matter version of dark matter theory with heavy (ca. 100 GeV) weakly interacting massive particles (called WIMPs), particularly evidence from the large scale structure of the universe. “Warm dark matter” theories appear to be a better fit to the data than either “cold dark mater” (with heavier, slower moving dark matter particles) or “hot dark matter” (with electron neutrino sized dark matter particles moving at close to the speed of light). See for example regarding dwarf galaxies: http://www.sciencedaily.com/releases/2011/10/111017124344.htm and http://arxiv.org/abs/1109.3187

    2. The most commonly modeled spherical distribution of dark matter in spiral galaxies (the “dark matter halo”) has also recently been falsified both with models of its effects and with detailed Milky Way rim astronomy measurements that rule out such large quantities of dark matter in the galactic rim in the vicinity of the solar system, see, e.g. http://www.eso.org/public/archives/releases/sciencepapers/eso1217/eso1217.pdf (a result confirmed by some, but not all, direct dark matter detection experiments). The observed dark matter distribution in spiral galaxies appears to be close to cones around the axis of the galaxy through the central black hole of the galaxy.

    3. Particle accelerator experiments like those at the large hadron collider (LHC) have ruled out all of the most plausible and well motivated fundamental particle candidates that interact via the weak force for dark matter with masses in a range consistent with cold dark matter or warm dark matter. There are also no known stable composite particles with the right mass for either theory.

    4. A fairly recent discovery revealed that the amount of ordinary baryonic matter in elliptical galaxies (one of two main galaxy types, spiral galaxies like our own are the other) was dramatically undercounted (http://washparkprophet.blogspot.com/2010/12/lots-of-dark-matter-actually-just-dim.html quoting a now closed access article) when the overall dark matter proportion in the universe canonically cited was developed and that therefore estimates of the amount of dark matter in the universe as a whole. The new data suggest an overall dark matter v. ordinary matter ratio closer to 50-50, than the canonical account in which there is far more dark matter than ordinary matter.

    5. There is a legitimate reason to think that estimates of the gravitational effects in spiral galaxies due to unmodified general relativity (e.g. GR says the kinetic energy and angular momentum of particles give rise to gravity, which isn’t the case in Newtonian gravity), which is often approximated with purely Newtonian gravity. Published papers estimating the phenomenological difference between Newtonian gravity and general relativity in a spiral galaxy vary widely. Some see no effect, some see this accounting for most of the effects otherwise attributable to dark matter. All models have to make simplifying assumptions to make a phenomenological prediction and there is dispute over whose simplifying assumptions are closest to the truth.

    6. In the last few years we have learned more about the impact of matter ejected from black holes at the centers of galaxies (aka ultra-fast outflows), and about the fine detail of the make up galactic clusters (see http://www.newscientist.com/article/mg21328465.800-mundane-dark-matter-may-lurk-in-starry-clusters.html) than we knew in the past. Black holes eject more matter in different directions and at different speeds than previously known and this has more of an influence of the shape of the bulge at galactic centers than previously known.

  71. ugh, I would have posted the actual link, but it keeps getting marked as spam…


    I agree with option number 2 above…
    “Sean, March 6:

    Hi Stacy–

    I’m not sure what you are saying about the third peak in the CMB. We agree that “pure baryons shouldn’t do that.” I can only think of three possibilities.

    (1) There is some sort of source for gravity other than baryons.
    (2) There is a modification of gravity that doesn’t include new sources, but also doesn’t respond directly to where the sources actually are.
    (3) The data aren’t good enough to say that the odd-numbered peaks are boosted relative to what we would expect from damped oscillations of baryons alone.”

    Keep in mind that it was an electrical engineer who nagged Einstein into the cosmological constant; if you accept that it’s making a come back.

  72. “Keep in mind that it was an electrical engineer who nagged Einstein into the cosmological constant; if you accept that it’s making a come back.”

    Who was that?

  73. It was one of the workers at his family’s electrical business;

    “The Einstein brothers’ Munich electrical engineering firm built and installed dynamos, power plants, and electric lighting systems, largely invented and patented by Albert’s uncle Jakob (1850– 1912), an engineer.”

    I don’t believe it was a family member…I’m looking for the exact name right now. It was after the business was moved to Italy. Maybe I’m thinking of Florence McKenzie from Australia. I thought it was an Italian Man who kept nagging him about some “force of the universe” and that Al eventually gave in and published something primarily to get him to shut up about it.

  74. This whole debate is very semantic. Two things appear clear to me. Apart if one gets into the realm of (crazy?) non-local theories, or if one doesnt believe WMAP (PLANCK, please hurry up), new fields are definitely required, and they must act as non-baryonic dark matter to explain the CMB. Full stop. On the other hand, the gravitational field in galaxies is quite intimately linked to the distribution of baryonic material in a way which is extremely hard to understand without invoking bizarre interactions between the above new fields (which cannot be plain CDM in that case) and the baryonic material, interactions acting in a way as to effectively produce the effect of a modified gravity law on galaxy scales, aka MOND. Full stop. So, that’s where we stand (see http://arxiv.org/abs/1112.3960 already mentioned by Stacy), and the question is where to go from there. My answer would be: “To the blackboard” ;)

  75. @ben

    I agree with you. Summary:

    You said: “(…)This whole debate is very semantic.(…)”
    Yes, that is the point I commented before.

    Your two “facts” that I am also quite sure phenomenology seems to tell us, in short words.:

    a)DM fields. New fields are definitely required and they must act as non-baryonic dark matter to explain the CMB.

    b) Gravitational field in galaxies. They interacts is such a way that the baryonic material acts effectively like a theory of a modified gravity law on galaxy scales, i.e., MOND.

    I am just wondering, seeing the whole discussion, and seeing the nice chart that Stacy made, if a) and b) are indeed incompatible or somehow complementary hypothesis, two aspects of the same unknown theory/model X. That is, could DM and MOND simultaneously exist? Or likely more precisely, can a DM-like theory provide a MONDian law?Can a MONDian theory provide DM fields?

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  77. @85: Please provide a reference. I have read several biographies of Einstein and have never heard anything even remotely similar to this. His motivations for introducing the cosmological constant are well known.

  78. @Riemannium: could DM and MOND simultaneously exist? Yes (http://arxiv.org/abs/0811.3143). Or likely more precisely, can a DM-like theory provide a MONDian law? Yes (http://arxiv.org/abs/0901.3114). Can a MONDian theory provide DM fields? This is almost always the case (TeVeS, non-canonical Einstein-Aether theories, etc., all harbor new fields that can act as DM). Even in the bimetric approach of MOND (http://arxiv.org/abs/1006.3809), there can be “twin matter” which can act as traditional DM to seed the growth of structure. I’m not saying any of the above solution is the correct one, most probably not, because they all have their own problems. Just that, in principle, it’s possible.

  79. @ben

    Yes, I did know those papers. I try to keep updated in Cosmology stuff.

    I know there are lots of cosmologists that argue strongly against MOND. Specially with arguments relative to Occam’s razor and similar simplifications. But Sean is also very clever and we should agree on his wise words that we should accept what data are telling us (of course, after Planck releases new data, I suppose we will be again discussing on the 3rd peak in the CMB spectrum-or not- and about what Planck is going to surprise us all).

    The main point AFTER accepting data as they are is to interpretate them! Looking backwards in time, remember that after Einstein formulated the correct till now version of the relativity principle and its consequences, ether’s theories were yet thought to be true in spite of the Michelson Morley experiment said that there were no delay in the speed of light ( no fringes in their experiment).

    So, maybe we are yet in a similar position. Very similar indeed. We are discussing data with some of our best paradigms (MONDs and CDM) but they find problems.

    Michelson-Morley experiment indeed produced the hypothesis on the LOrntz-Fitzgerald contraction and time dilation to explain why ether was no detected. However, Einstein realized that the ether was not necessary at all. He only provided the correct theory.

    Let me speculate a bit more. Accepting data, what kind of theory X should a theorist try to build in order to “be happy enough”?Hard problem, since, it seems:

    0)Theory X MUST explain every observational data from Cosmology and Astrophysics we know are right.
    1)Theory X includes a MOND-like revision of newtonian gravity at galactic scales.
    2)Theory X can be interpreted as DM particles or likely include a DM component at the CMB level to explain it.
    3)Theory X should explain extra astrophysical stuff.
    4)Theory X could include (likely) a Dark Energy explanation.
    5)Theory X will change our current Cosmological misconceptions and provide a bigger portrait of the Early Universe.

  80. @Riemannium: yes, to my mind, while plain CDM is wrong, the non-baryonic DM and MOND concepts, while not necessarily mutually exclusive, are more likely both unveiling different aspects on different scales of a theory X which does not exist yet: so “to the blackboard” indeed

  81. Sean Carroll writes:

    there is ample evidence of gravitational forces pointing in directions where there isn’t any (ordinary) “stuff” to create them, leading us to accept the existence of some form of dark matter.

    This kind of ‘evidence’ was introduced in 2006 by Clowe et al. in their “A direct empirical proof of the existence of dark matter”, but their proof is totally incorrect. As shown in MOND and DM… the nonlocal effects associated to the modification of gravitation “can be spatially segregated from the observable baryonic mass”.

  82. This entire discussion proceeds from the point-of-view that the presence of matter is causative of the curvature of spacetime that we perceive as gravity, and also that it does so essentially according to the Einstein field equation G equals 8*pi*T.

    It’s as if you assume that without the presence of matter, spacetime would be perfectly free of gravitational ripples, including the extreme case of singularities that seem to be at the heart of every galaxy. Why must this be so?

    Is it not possible that the Big Bang event itself instantaneously initiated the rippling of spacetime up to and including the existence of singularities? And is it not further possible that, as the universe later cooled and matter precipitated into existence, a gravitationally-rippled spacetime became populated with matter that migrated (or “fell”) along these ripples towards pre-existing singularities?

    If this were the case, then there are three possible scenarios:

    The first is the case that there is precisely all the matter in a local spacetime environment that a local singularity can grasp, and no more matter than that. In short, this first case represents what we know and love as local equality between G and 8*pi*T.

    The second is the case that there is more matter in a local spacetime environment than a local singularity can grasp. In this case, the excess matter would not be bound to the local singularity and would be free to migrate to the environment of another neighboring singularity. Over time, the local environment around the local singularity would be cleared of all excess matter up to the point where, once again, there would eventually be local equality between G and 8*pi*T. In short, this second case implies that when 8*pi*T starts out locally greater than G, it eventually decays into the first case where equality between G and 8*pi*T holds locally, and eventually, the local environment appears to be as we know and love it.

    The third case is the interesting one in which there is less matter in a local spacetime environment than a local singularity can grasp. In this case, there would appear to be gravity in excess of that expected to be caused by the matter perceivable to a distant observer working with an assumption of equality between G and 8*pi*T and assuming that it is matter that causes the gravitational rippling of spacetime. In short, this third case would suggest to a distant observer that G is locally greater than 8*pi*T, and further suggest to that distant observer that he posit the existence of a mysterious “invisible” form of matter to restore local equality. This third local environment is one that we do not know or love at all. It confuses us because we assume that G equals 8*pi*T everywhere and we assume that the existence of matter precedes the existence of gravitational rippling.

    In summary, if the Big Bang event initiated extreme rippling of spacetime (i.e. gravity) before the precipitation of matter began to ride those ripples, then after 13.7 billion years, the universe might very well appear to us to be locally smooth in many environments, but in need of some invisible matter in other environments to explain an apparent local glut of gravity.

    In short, I propose that the Einstein field equation be modified to G>=8*pi*T, and that the Dark Matter Theory to explain excess gravity be scrapped.

  83. I strongly agree with Sean that the scalar fields in any “modified gravity” theory are just another name for dark matter (or dark energy, the two are rather degenerate, see Kunz, say).

    How does any MOND theory attempt to answer any of the problems that particle physics theories that predict DM answer, namely the strong CP problem (look it up) and the hierarchy problem? Are we to assume Nelson-Barr and technicolor (is a technibaryon a dark baryon or non-baryonic?), or is ADD (Arkani-Hamed-Dimopoulos-Dvali extra dimensions) “modified gravity”? Where are all the axions in MOND?

    I also (in a terrible bias towards my own work) think that light scalar fields working as Hu’s F(uzzy)CDM are natural, and should predict very different non-linear structure formation due to coherent pressure than a dark sector composed entirely of dust CDM (in large scale structure this is similar to warm dark matter). I don’t know what this is, and would like to work to find out, but I don’t find the admixture of such a component to ordinary CDM at all baroque. Since these properties are somehow “quantum” and set preferred length scales then I don’t find the fix too outlandish to expect. Any non-WIMP DM component should have some effect on galaxy dynamics, surely? Disclaimer: I know next to nothing about galaxy dynamics and this is just a hunch.

    I see this, unscientifically and just by way of coincidence, as kind of related to what was said about atoms earlier in these comments, and interestingly related to the “Quantum Mechanics when you close your eyes” May 25th post. Quantum Mechanics to fix your galaxy dynamics!

  84. If gravity is confined in some restricted area, it works stronger. Then Dark Matter is not needed. It is said that Gravity spreads eaqually three dimensinally. But if it stays inside the pizzalike shape, it spreads two dimensinally, and it works on 1/r base, Flat rotation curve will be naturally obtained.

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  87. Wait !!

    The Noble Laurate, Gerardus ‘t Hooft in a 2008 paper stated that the abscence of matter does not guarantee flatness. I took this a step further and showed that gravitational accelration can be determined without knowing the mass of the planet or star, by the simple equation g=(tau).c^2 where tau = change in time dilation divide by the change in distance.

    I’ve published my 12-year study into gravity modification titled “An Introduction to Gravity Modification”

    Publisher’s web site http://www.universal-publishers.com/book.php?method=ISBN&book=1612330894

    Foreword by astrophysicist, Dr. Andrew Beckwith. More info at http://www.iseti.us/