Dark Photons

It’s humbling to think that ordinary matter, including all of the elementary particles we’ve ever detected in laboratory experiments, only makes up about 5% of the energy density of the universe. The rest, of course, comes in the form of a dark sector: some form of energy density that can be reliably inferred through the gravitational fields it creates, but which we haven’t been able to make or touch directly ourselves.

It’s irresistible to imagine that the dark sector might be interesting. In other words, thinking like a physicist, it’s natural to wonder whether the dark sector might be complicated, with a rich phenomenology all its own. And in fact there is something interesting going on: over the last 15 years we’ve established that the dark sector comes in at least two different pieces! There is dark matter, 25% of the universe, which we know is like “matter” because it behaves that way — in particular, it clumps together under the force of gravity, and its energy density dilutes away as the universe expands. And then there is dark energy, 70% of the universe, which seems to be eerily uniform — smoothly distributed through space, and persistent (non-diluting) through time. So, there is at least that much structure in the dark sector.

But so far, there’s no evidence of anything interesting beyond that. Indeed, the individual components of dark matter and dark energy seem relatively vanilla and featureless; more precisely, taking them to be “minimal” provides an extremely good fit to the data. For dark matter, “minimal” means that the particles are cold (slowly moving) and basically non-interacting with each other. For dark energy, “minimal” means that it is perfectly constant throughout space and time — a pure vacuum energy, rather than something more lively.

Still — all we have are upper limits, not firm conclusions. It’s certainly possible that there is a bushel of interesting physics going on in the dark sector, but it’s just too subtle for us to have noticed yet. So it’s important for we theorists to propose specific, testable models of non-minimal dark sectors, so that observers have targets to shoot for when we try to constrain just how interesting the darkness really is.

Along those lines, Lotty Ackerman, Matt Buckley, Marc Kamionkowski and I have just submitted a paper that explores what I think is a particularly provocative possibility: that, just like ordinary matter couples to a long-range force known as “electromagnetism” mediated by particles called “photons,” dark matter couples to a new long-range force known (henceforth) as “dark electromagnetism,” mediated by particles known (from now on) as “dark photons.”

Dark Matter and Dark Radiation
Authors: Lotty Ackerman, Matthew R. Buckley, Sean M. Carroll, Marc Kamionkowski

We explore the feasibility and astrophysical consequences of a new long-range U(1) gauge field (“dark electromagnetism”) that couples only to dark matter, not to the Standard Model. The dark matter consists of an equal number of positive and negative charges under the new force, but annihilations are suppressed if the dark matter mass is sufficiently high and the dark fine-structure constant $hatalpha$ is sufficiently small. The correct relic abundance can be obtained if the dark matter also couples to the conventional weak interactions, and we verify that this is consistent with particle-physics constraints. The primary limit on $hatalpha$ comes from the demand that the dark matter be effectively collisionless in galactic dynamics, which implies $hatalpha$ < 10-3 for TeV-scale dark matter. These values are easily compatible with constraints from structure formation and primordial nucleosynthesis. We raise the prospect of interesting new plasma effects in dark matter dynamics, which remain to be explored.

Just to translate that a bit, here is the idea. We’re imagining there is a completely new kind of photon, which couples to dark matter but not to ordinary matter. So there can be dark electric fields, dark magnetic fields, dark radiation, etc. The dark matter itself consists half of particles with dark charge +1, and half with antiparticles with dark charge -1. Now you might say to yourself, “Why don’t the particles and antiparticles all just annihilate into dark photons?” That kind of thinking is probably why ideas like this weren’t explored twenty years ago (as far as we know). But if you think about it, there is clearly a range of possibilities for which the dark matter doesn’t annihilate very efficiently; for example, if the mass of the individual dark matter particles was sufficiently large, their density would be very low, and they just wouldn’t ever bump into each other. Alternatively, if the strength of the new force was extremely weak, it just wouldn’t be that effective in bringing particles and antiparticles together.

None of that is surprising; the interesting bit is that when you run the numbers, they turn out to be pretty darn reasonable, as far as particle physics is concerned. For DM particles weighing several hundred times the mass of the proton, there should be about one DM particle per coffee-cup-sized volume of space. The strength of the dark electromagnetic force is characterized, naturally, by the dark fine-structure constant; remember that ordinary electromagnetism is characterized by the ordinary fine-structure constant α = 1/137. It turns out that the upper limit on the dark fine-structure constant required to stop the dark matter particles from annihilating away is — about the same! I was expecting it to be 10-15 or something like that, and it was remarkable that such large values were allowed.

However, we know a little more about the dark matter than “it doesn’t annhilate.” We also know that it is close to collisionless — dark matter particles don’t bump into each other very often. If they did, all sorts of things would happen to the shape of galaxies and clusters that we don’t actually observe. So there is another limit on the strength of dark electromagnetism: interactions should be sufficiently weak that dark matter particles don’t “cool off” by interacting with each other in galaxies and clusters. That turns into a more stringent bound on the dark fine-structure constant: about an order of magnitude smaller, at $hatalpha$ < 10-3. Still, not so bad.

More interestingly, we can’t say with perfect confidence that the dark matter really is effectively non-interacting. If a model like ours is right, and the strength of dark electromagnetism is near the upper bound of its allowed value, there might be very important consequences for the evolution of large-scale structure. At the moment, it’s a little bit hard to figure out what those consequences actually are, for mundane calculational reasons. What we are proposing is that the dark matter is really a plasma, and to understand how structure forms, one needs to consider dark magnetohydrodynamics. That’s a non-trivial task, but we’re hoping it will keep a generation of graduate students cheerfully occupied.

The idea of new forces acting on dark matter is by no means new; I’ve worked on it recently myself, and so have certain co-bloggers. (Strong, silent types who are too proud to blog about their own papers.) What’s exciting about dark photons is that they are much more natural from a particle-physics perspective. Typical models of quintessence and long-range fifth forces invoke scalar fields, which are easy and fun to work with, but which by all rights should have huge masses, and therefore not be very long-range at all. The dark photon comes from a gauge symmetry, just like the ordinary photon, and its masslessness is therefore completely natural.

Even the dark photon is not new. In a recent paper, Feng, Tu, and Yu proposed not just dark photons, but a barrelful of new dark fields and interactions:

Thermal Relics in Hidden Sectors
Authors: Jonathan L. Feng, Huitzu Tu, Hai-Bo Yu

Dark matter may be hidden, with no standard model gauge interactions. At the same time, in WIMPless models with hidden matter masses proportional to hidden gauge couplings squared, the hidden dark matter’s thermal relic density may naturally be in the right range, preserving the key quantitative virtue of WIMPs. We consider this possibility in detail. We first determine model-independent constraints on hidden sectors from Big Bang nucleosynthesis and the cosmic microwave background. Contrary to conventional wisdom, large hidden sectors are easily accommodated…

They show that these models manage to evade all sorts of limits you might be worried about, from getting the right relic abundance to fitting in with constraints from primordial nucleosynthesis and the cosmic microwave background.

Our model is actually simpler, because we have a different flavor of fish to fry: the possible impacts of this new long-range force in the dark sector on observable cosmological dynamics. We’re not sure yet what all of those impacts are, but they are fun to contemplate. And of course, another difference between dark electromagnetism and a boring scalar force is that electromagnetism has both positive and negative charges — thus, both attractive and repulsive forces. (Scalar forces tend to be simply attractive, and get all mixed up with gravity.) So we can imagine much more than a single species of dark matter; what if you had two different types of stable particles that carried dark charge? Then we’d be able to make dark atoms, and could start writing papers on dark chemistry.

You know that dark biology is not far behind. Someday perhaps we’ll be exchanging signals with the dark internet.

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74 Responses to Dark Photons

  1. V says:

    If the dark matter particles belong to a hidden sector, then they would also be charged under whatever the hidden sector gauge group happens to be, and so there could be strong interactions between the dark matter particles not just from the U(1). Haven’t such particles already been considered in the hidden sector of string theory models?

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  2. Sean says:

    Sure. There’s been a decent amount of work on what would happen if a new short-range force coupled to dark matter, which is what you would tend to get with strong gauge groups (or spontaneously broken ones). The new thing here is a long-range, non-scalar interaction. (Of course the new U(1) symmetry could come from some string or GUT model, which would be another interesting thing to think about.)

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  3. From a non-physicist: I don’t feel humbled at all given that the complexity of life has arisen in (what’s the word for?) regular matter. Even if dark matter and dark energy are more complex than expected, surely intelligence can’t develop from them (skipping all the Tao of Physics stuff)?

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  4. GP says:

    Robert J Sawyer’s novel Starplex featured some dark biology—planet sized creatures that intentionally shaped galaxies into spirals because they were prettier that way. I’m sure its full of inaccuracies—they communicated via radio, if I remember correctly, which isn’t very dark of them—but an oddball connection to this idea nonetheless!

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  5. noname says:

    Hi Sean.

    I have what I hope is a straight forward question. In this model, is dark matter a thermal relic? And if so, shouldn’t you have a corresponding dark CMB? If the dark matter is in thermal equilibrium with regular matter early on, it seems it should be in equilibrium with a dark photon sea, and while the extra degrees of freedom might not be enough to significantly alter BBN, could they alter the epoch of matter-radiation equality, thereby severely distoring the good old CMB?

    Thanks in advance.

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  6. Sean says:

    Absolutely, there will be dark background radiation. But the dark sector (dark matter + dark radiation) decouples relatively early on (temperatures of order 10 GeV). After that, energy gets dumped into ordinary photons from other standard-model particles, but not into the dark photons; so soon, the dark temperature is lower than the ordinary temperature. That’s why there is no problem with BBN or the CMB.

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  7. Dark light? I’ll believe it when I see it.

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  8. TimG says:

    Hi, Sean. I have a basic question. You mentioned that if the density of dark matter is sufficiently low, it won’t annihilate much. But why doesn’t dark matter clump together into higher density objects, the same way ordinary matter clumps together into stars? I mean, the clumping together of ordinary matter is just due to gravity, right? And dark matter feels gravity too.

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  9. adonais says:

    Interesting stuff. But the dark-name scheme doesn’t work. I suggest “delectromagnetism” and “phonots.” I hope you can shed some d-light on d-matter. Let there be d-light. Ahem.

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  10. Howabout “phonoffs?”

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  11. I mean photoff. Whatever.

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  12. Sean says:

    TimG– Yes, there will be some annihilations, just as there are for weakly-interacting dark matter particles as dark matter candidates. And our DM will clump, just like non-interacting DM. But, they’re very rare for the parameters that are allowed by galactic dynamics, at the densities we have in real galaxies; in particular, they don’t change the total DM abundance in any significant way.

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  13. TimG says:

    And one more question, if you don’t mind: If dark matter turns out to be a superpartner of regular matter, then wouldn’t we expect the corresponding regular matter to also have a “dark charge”?

    In other words, I’m wondering if the idea of a force that only effects dark matter is incompatible with the idea that dark matter has a regular matter superpartner.

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  14. TimG says:

    Sean, thanks for your answer to my first question. I guess what I’m really wondering is just how “clumped up” dark matter is in comparison to normal matter.

    Allow me to clarify by telling you a bunch of stuff you of course already know:
    The average density of ordinary matter in the galaxy is pretty low, since the galaxy contains lots of empty space (empty of ordinary matter, at least). But most of that matter finds itself in stars and such where the density is much higher. So the average distance between a typical particle of matter (i.e., one that resides in a star) and its nearest neighbors is much less than you’d get from just looking at the average density of the galaxy as a whole. So it seems to me it’s the density of matter in stars that you’d need to look at to know how likely a typical particle is to get close enough to interact with another particle.

    So when you give a figure like “one dark matter particle per coffee cup sized volume”, are you telling us the average density of dark matter in a typical galaxy, or are you telling us the density in a “star-sized clump” of dark matter? That is, if dark matter even comes in star-sized clumps. If it doesn’t clump up that much but instead is pretty uniformly spread throughout the galaxy, then I’m wondering “How come?” Shouldn’t gravity make dark matter clump up to much the same degree as regular matter?

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  15. Serge says:

    Another layman question:
    Are you saying that dark energy, or part of it could be not cosmological constant or scalar field/quintessence, but dark photons instead ? That is the same nature as dark matter.

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  16. Jason Dick says:


    No, that doesn’t work. Dark photons would drop off with the expansion of the universe in the exact same way that normal photons do (as the scale factor to the fourth power). Dark energy requires that the energy density be approximately constant with the expansion.

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  17. Lab Lemming says:

    “interactions should be sufficiently weak that dark matter particles don’t “cool off” by interacting with each other in galaxies and clusters.”

    If dark matter doesn’t cool off, then how did it get cold enough to stay gravitationally bound in galaxies? Or was in much colder than everything else way back when the Big Bang was still just mediocre sized?

    Also, would dark particle/antiparticle pairs allow black holes to emit dark Hawking radiation? I recommend building a little one at the LHC to experiment on.

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  18. Arun says:

    Sorry, should check your paper, but asking here – is the dark charged matter fermionic or bosonic?

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  19. ObsessiveMathsFreak says:

    I must confess to being a long term dark matter skeptic, at least when it comes to these kinds of “magic particle” interpretations. We can’t even create or directly examine dark matter, and the only evidence for it comes from cosmological studies which seem _very_ unlikely to provide any information at all about microscale dark matter interactions. I think postulating dark particles and anti-particles, etc, is really stretches this topic into the grossly speculative regions inhabited by the likes of String Theory.

    That said, I am effectively a layman when it comes to cosmological models, so my knowledge of dark matter is only informed by what are essentially popular science materials. Hence my skepticism. I for one would appreciate seeing introductory material, or references to some, that discusses dark matter without fear of presenting concrete equations and models, showing clearly why classical models fail and why dark matter is needed. So far, I have been unable to find any such presentation, not even so much as a basic gravitational model. I think that the lack of such a presentation, passed over in favour much less rigorous ones, is the reason that you see a lot of skepticism on this topic.

    Also, a small point, but I think the physics community may have already been beaten to the dark particle zoo hypothesis by the Fleetmind.

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  20. Jason Dick says:

    Lab Lemming,

    Everything cools with the expansion of the universe. This is how dark matter cooled. As long as it’s produced and decoupled from the visible sector early enough, it’s quite cool even before the emission of the CMB. I presume what Sean is talking about with respect to galaxies and clusters is radiative cooling, where the cluster dark matter would lose energy by emitting radiation (in this case, dark photons). And as long as this hypothetical new force is weak enough, that will happen slowly enough that we wouldn’t have yet detected it.

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  21. Count Iblis says:

    If the DM in this model also interacts with ordinary matter via the weak interaction, then won’t the DM get an effective ordinary (milli)charge due to radiative corrections, similar to what happens in this case?

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  22. Elayne Riggs says:

    I remain convinced that this dark matter fad is something totally created out of thin air (if you’ll pardon the expression) so scientists can make their sums add up, and they’re all going to look very foolish in another few decades…

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  23. Xenophage says:

    Have you rediscovered “mirror matter”? The Fine Structure constant is then already installed,


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  24. Shantanu says:

    Sean, u probably missed a reply to my earlier comment about Blanchet’s model of dark matter. Is that ruled out by Bullet cluster and would this also have the same dark properties discussed in your paper?

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  25. Sean says:

    Thanks for the references, everyone, we will look them over. I wouldn’t be surprised if we missed some very referenceable stuff, but we did ask around to see if this particular idea had been examined before, and as far as we can tell it hasn’t. Again, the idea of interactions (even long-range U(1) interactions) in the dark sector is not new, but I think we are the first to take seriously the astrophysical consequences of such a force.

    TimG– Sure, the dark matter density is much higher in the center of a galaxy or cluster than it is in an average spot in the universe. But once you check the numbers, it’s still not nearly high enough for interactions to be significant — that’s one of things we checked.

    Lab Lemming– Jason is right, this is “cold” dark matter, but I was thinking of cooling in the context of galactic dynamics. Baryons cool off through dissipation and settle to the bottom of gravitational potential wells very efficiently; you don’t want the DM to do that, or it’s incompatible with observations.

    Arun, the DM can be either fermionic or bosonic.

    Count Iblis– That’s a good question, and we examined the possibility of dark E&M mixing with ordinary E&M. If they don’t mix at very high energies, we verified that there is no mixing induced at low energies; that’s just how the Feynman diagrams work out. So why don’t know why they don’t mix at high energies, but at least the setup is stable under quantum corrections.

    Shantanu– We checked against various limits on the DM interaction cross-section, including the bullet cluster.

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  26. Lawrence B. Crowell says:

    I have not read this paper yet. I must confess that I wonder where the additional U(1) comes from. I suppose maybe it is from a mechanism similar to some U(n) breaking into n copies of U(1).

    If dark matter is some SUSY partner, or composite such as the neutralino, then is this U(1) gauge boson also a vector boson which is paired up with a fermion? Further, I wonder about the charge. There must be a charge which defines the source for this field. If the currents associated with this field, some form of divE = rho or int B*da = oint J*dx, are associated with SUSY partners, then this charge should be present in ordinary matter. SUSY transformations don’t wipe away charges.

    Lawrence B. Crowell

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  27. Sean says:

    Yes, I forgot to mention: our DM candidate is certainly not some superpartner of any of the particles in the Standard Model, since we don’t want any of them to carry dark charge.

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  28. ObsessiveMathsFreak says:

    Jason Dick

    See http://arxiv.org/abs/0803.0556.

    A few minutes googling turned up this resource on Dark Matter. The authors claims that existing results justifying dark matter are based on the assumption that classical models predict Keplerian dynamics for galactic disks, i.e. that the orbits of stars in the galactic disk should behave like planetary orbits in a solar system with increasing distance. This talk by V. Rubin from 2000 also seems to confirm that this is the general assumption among astronomers, and that failure of galactic rotations to fit this Keplerian model is taken as evidence for dark matter.

    As Feng and Gallo point out in their paper above, this assumption that Keplerian dynamics should apply to galactic disk is really not justified. Quite a brief investigation of the integrals involved will show that the Shell theorem does not apply to 2 dimensional discs, which Galaxies more or less are, we should not expect at all that velocities will obey a Keplerian profile, and should not really be surprised when they don’t.

    It seems that this assumption may be due to the fact that calculating the gravitational forces of 2D discs involves evaluating elliptic integrals which have singularities at their boundaries, a task which only really became open to general investigation in the last ten years or so with the advent of personal computers and computer algebraic and numerical programs. Prior to this, evaluations of such integrals would have required a not insubstantial budget, so it would not be surprising to find that the Keplerian assumption was never subjected to much scrutiny.

    The forumulae in the Feng and Gallo paper are (integrations excepted) quite elementary. In the paper in fact, they attempt to solve the inverse problem of determining the galactic mass density from the observed velocity profile.

    Given the seemingly mistaken assumptions of astronomers that Keplerians dynamics should apply to disks, one must also wonder about the assumptions made of Galactic clusters, composed as they are of these two dimensional discs which do not behave as spherical attractors.

    Anyway, as I mentioned before, astronomically speaking, I am a lay person, so I will stop there, and remind the reader that my assessment is not a fully informed one. Still, I think that it would be worth reviewing some of the “settled” concepts in astrophysics using the tools and methods which have become available over the last 80 or so years. We have the technology.

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  30. Sili says:

    I’m onto you. Next you’ll team up with Phil Plait and discover away for this new and improved dark stuff to destroy Earth and, hey presto!, you’ll be wanting to be made professors of Defence Against the Dark Arts.

    there should be about one DM particle per coffee-cup-sized volume of space.

    Espresso or cappouchino?

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  31. Lawrence B. Crowell says:

    Sean: Yes, I forgot to mention: our DM candidate is certainly not some superpartner … .

    This reminds me of an idea I had some years ago where quantum field theory was fundamentally octonionic, where there are 7 copies of quaternions. Each of these copies “defined” a “standard model,” but they only transformed between each other by very weak interactions that are nonassociative. I gave up on the idea, but I played with the idea that there exist 6 other “gauge worlds” which collectively composed what we call dark matter.

    What ever this dark matter is it clearly does not dissipate energy much, such as EM radiation emitted by hot plasmas and the rest. In order for gravity to clump matter into small volumes you need this sort of mechanism. Dark matter particles then appear to largely orbit around without giving up their energy and so DM clouds are diffuse and extensive.

    For your model to hold, what do you propose as the charge sources, or the dark matter fermions analogous to electrons etc which carry this additional U(1) charge?

    Lawrence B. Crowell

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  32. Aiya-Oba says:

    Congratulations Sean, I think you have discovered a whole new world is Astrophysics.-Aiya-Oba(Poet/Philosopher).

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  33. Jason Dick says:


    You could have actually read the link before typing such a long post. It had precious little to do with galaxy rotation curves. Galaxy rotation curves are only one small piece of evidence for dark matter, and if that’s the only evidence we had, we wouldn’t be nearly so confident that it’s out there.

    That aside, however, the reason why astronomers believe that galaxy rotation curves should at least approximately follow Keplerian dynamics is because the majority of the stars in most galaxies is near the core. The density of stars falls off dramatically with distance from the center, so the fact that spiral galaxies are disk-like is actually a pretty small effect. Furthermore, the galaxy rotation curves have been also shown to be inconsistent with Newtonian physics in elliptical galaxies.

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  34. milkshake says:

    What if there was a DM/anti-DM asymmetry and all massive DM particles happened to have the same “dark charge” sign so that the “dark electromagnetism” effectively acted as a repulsive interaction? Would this fit the observed DM distribution in the galaxies?

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  35. Lawrence B. Crowell says:


    This is a very good point. If there are dark charges q_d then there have to be an equal number of opposite charges -q_d. Why? Imagine there is a space with only one charge on it. Suppose the space is a sphere. Then in a classical picture the lines of force leave all these charges and have “nowhere to go.” These lines of charges would wind around the space densely and some thought should indicate this is a divergence! If the space is flat the problem still remains, for you end up with a divergent field density “at infinity.” So from a topological vector field perspective lines of force which leave some source must terminate at an opposite charge.

    So there have to be opposite dark charges in this model. The question is whether the dark matter particles are particle-antiparticle pairs or not. The data is not entirely clear as yet. The article by Cirelli et. al http://arxiv.org/abs/0809.2409 reports on PAMELA data which suggest ~1 TeV DM-antiDM annihilations. Of course this does not lend weight one way or the other for this dark U(1) theory, but if this theory is right it might lend support for anti-DM particles with opposite dark charges. On the other hand, we might find the oppositely charged DM have to be at least in part due to some some other species. If this is the case this would suggest that dark matter corresponds to some alternate particle-gauge “world” coupled to our world largey by gravitation and very weakly by maybe some other processes. Will the LHC resolve some of these questions?

    Lawrence B. Crowell

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  36. sleep says:

    Is it possible to test these ideas using the LHC? Why not?

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  37. Lawrence B. Crowell says:

    We might be able to produce dark matter in the LHC. The Pamela results give a possible hint that we might be able to get dark matter at the TeV range. Of course if we produce dark matter particle we might have a devil of a time detecting them. It took 40 years to get the neutrino more or less figured out and figuring out the nature of dark matter particles could turn out to be much the same story.

    Lawrence B. Crowell

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  38. Lab Lemming says:

    Assuming that a dark matter observer couldn’t interact with our EM, strong, and weak forces, could they see the gravitational signal of light matter? Or would they have to be unlucky enough to wander past a star in order to notice it?

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  39. Sean says:

    In principle, dark astronomers doing very high-precision cosmology could certainly observe the existence of “ordinary” matter via its gravitational field. In practice, there aren’t going to be any dark observers, as the dark matter has to interact pretty weakly to be consistent with our observations, and that makes it very difficult to make an observer.

    Unfortunately there don’t seem to be any particle-physics signatures of this model. Again, the coupling to dark photons is pretty small, so dark matter particles will behave pretty much like ordinary WIMPs in the LHC or elsewhere. It might be possible to detect the dark matter, but it would be extremely hard to tell that there were such things as dark photons.

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  40. Zenshadow says:

    I’m a layman to physics. Just Joe the Layman here. I was wondering if there had been any studies done to see if there is a link between when Inflation began (immediately following the big bang) and the ‘disappearance’ of anti-matter. Could they be aspects of the same event? The conversion of all that anti-matter to energy would power the inflation is my hypothesis. You can include me in any paper that gets published on this concept, lol.

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  41. Quasar9 says:

    oops I just realised this post is two days old.
    Happy Halloween!

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  42. S Halayka says:

    This is very interesting work…

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  43. Pingback: Heb je ook donkere fotonen? en Astroblogs

  44. tyler says:

    a golden age for Cosmic Variance! so many interesting posts and so little comments trolling!

    I have been working for 6 months just to formulate this idea as a question intelligent enough to ask here – and now here is the answer! Fascinating and very much appreciated!

    regarding the last paragraph in your initial post, sean, any dark biology would soon imply dark sex, which would of course provide 98% of the content in the dark internet.

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  45. tyler says:

    too many exclamation points! too much strong Portland coffee!

    sorry about that

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  46. Marshall says:

    Interesting paper.

    You should also consider solar system bounds on dark matter. This can be done in a number of ways – by comparing the mass of Earth as seen from the Moon and as from Lageos (Adler, S.A., J. Phys. A: Math. Theor. 41 (2008) 412002, or http://arxiv.org/pdf/0808.0899) or the disturbance in solar system celestial dynamics (http://arxiv.org/pdf/0806.3767, http://arxiv.org/pdf/0810.2827), or on its effects on the internal dynamics of the planets (http://arxiv.org/pdf/0808.2823).

    Remember that dark matter will clump gravitationally, which could have been important in the early universe and those clumps may have survived (Nature, VOL 433, 27 Jan 2005, 389). Such clumps will interact with normal matter gravitationally (if no other way), and that says that some fraction will be bound in structures with normal matter. If a dark matter clump comes through the solar system, and it gravitationally interacts with one of the planets, there is a chance that some of the clumps, or some portion of the clumps, will become gravitationally bound to the solar system, and thus detectable. (The same 3 body interactions will apply to individual dark matter particles if there is no clumping of dark matter.) Even if the rms velocity of the clumps is too high to make this very probable, 4.5 billion years is a long time and there will be a dark matter halo around the Sun, and maybe individual planets as well; this should be considered tests of dark matter.

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  47. Alsee says:

    Is it a reasonable hypothesis to suggest that there are N independent sets of matter of equal mass? Given the current estimated ratio of dark matter to normal matter that would set N equal to 7 or 8. That would mean our dark matter problem would actually be composed of 6 or 7 sets of dark matter, with each of them dark to each of the others. The only cross-interaction would be via gravity.

    If our dark matter is composed of 6 or 7 independent sets then the density within each set is far lower, and the viable strength of interaction would be much higher within each set of dark matter. It would be neat if the self-interactions within each were exactly mirrors of the forces and strengths within our “light matter”, but as I understand it I think that would cause way too much clumping in violation of observations.

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  48. Andrew P says:

    This idea of a second electromagnetism is not new. It actually dates from the 1950s which speculated on a mirror sector that would restore the global symmetries that are violated by neutrinos. A guy named Foot has publised a lot of papers on arxiv.org about mirror matter. I will point out that if the particle (atomic) masses are much larger than in the normal sector, mirror electromagentism could have a strength similar to our own, and still match observations. There is also no need for much mirror antimatter as mirror matter could have lost all antimatter by a mechanism similar to our own sector. If mirror atoms have a different mass, nuclear fusion, and thus stars made of mirror matter, might not exist. But even if there are no mirror stars, there should still be accretion phenomena, and they should emit dark sector light. A telescope that could see in mirror light might see nothing but quasars and glowing jets.

    How about something even wierder. Suppose that tachyons exist. Would a bound state of 2 tachyons itself be a tachyon? Or would it be a subluminal particle that is spread out over a large spatial volume. My gut tells me that it is the latter, but I do not know how to calculate this. If something like this exists, it could make for a very hard to detect form of dark matter.

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  49. Lawrence B. Crowell says:

    Dark matter might indeed be due to a range of different fields, from braney LambdaCDM, to SUSY pairs and maybe alternate gauge fields and particles. It could be a complex world of sorts. Since dark matter is weakly interacting I agree with Sean that it is not likely to lead to complex configurations requred for “dark observers.”

    Lawrence B. Crowell

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  50. Benjamin says:

    Quoted from Marshall:

    “If a dark matter clump comes through the solar system, and it gravitationally interacts with one of the planets, there is a chance that some of the clumps, or some portion of the clumps, will become gravitationally bound to the solar system, and thus detectable. (The same 3 body interactions will apply to individual dark matter particles if there is no clumping of dark matter.) Even if the rms velocity of the clumps is too high to make this very probable, 4.5 billion years is a long time and there will be a dark matter halo around the Sun, and maybe individual planets as well; this should be considered tests of dark matter.”

    There’d be an easy way to detect a dark matter halo around the Sun, in the orbits of the outer planets. Suppose it were uniform in density; then by Newton’s shell theorem, you should get a sunward force linearly increasing with distance from sun, then dropping off at some boundary. Now clearly, the density is likely to be higher closer to the sun, that was just an illustrative model. But that might show up, say, in the trajectories of the Pioneer and Voyager probes, accounting for some of the sunward acceleration.

    I like Alsee’s idea, too. Having interactions on the scale of ours would be exciting, suggesting there could be dark life, but I’d be curious as to what sort of chemistry could develop with a very low fine structure constant.

    Just one point. What about a dark colour force? It’s difficult enough as it is to make QCD calculations where we know what the answer should be; is it possible to exclude this based on astrophysical data? Because if you’re having strongly radiant bodies, either it’s going to be thermal, with pockets of very hot dark matter contracting, say, under their own gravity, or you’ve got to have nuclear or chemical reactions.

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  51. Lawrence B. Crowell says:

    If dark matter clusters around stars or stellar systems then we might get some F = -kr type of force inwards for bodies in the DM cloud and assuming a more or less constant density. If there is a dark matter particle in a coffee cup volume, as stated by Sean, then this is one particle per ~10cm^3. A spherical volume containing the solar system is about 10^{30}km^3 = 10^{45}cm^3. So that would amount to about 10^{22} moles of DM particles in the whole solar system. If the mass of DM particles is assumed to be ~ 1 TeV then this is about 10^{25} grams of the stuff within a sphere of 10^{10}km around the sun. This is a bit, but considering that the Earth is 10^{30}g in mass the total DM mass in the solar system is then comparable to one of the larger asteroids in the solar system.

    Of course we can play with the mass of DM particles and their distrubutions. I am also not sure whether this works for the Pioneer anomaly, which appears “device dependent,” as the Voyager crafts don’t appear to have this effect.

    Lawrence B. Crowell

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  52. Marshall says:

    If there is a dark matter particle in a coffee cup volume, as stated by Sean, then this is one particle per ~10cm^3. A spherical volume containing the solar system is about 10^{30}km^3 = 10^{45}cm^3. So that would amount to about 10^{22} moles of DM particles in the whole solar system. If the mass of DM particles is assumed to be ~ 1 TeV then this is about 10^{25} grams of the stuff within a sphere of 10^{10}km around the sun.

    This should understand the effect, as this is the background density, not the density of a solar DM halo. However, 10^22 Kg is about 5 x 10^-9 Msun or about 10 times the Mass of Ceres. Ceres can be detected at the few percent level in Earth-Mars ranging (the Ceres mass formal error is 7 x 10^-13 Msun in the EPM2004 ephemeris – see http://iau-comm4.jpl.nasa.gov/EPM2004.pdf). Note that 10^10 km ~ 67 AU, so there should be about 5 x 10^-12 Msun within 6.7 AU in this model.

    So, there is at least a potential for detectability – the real question IMHO is how concentrated a dark matter halo would be. Best for detectability would be a scale height of a few AU, but it would clearly be good to estimate that in a parameterized fashion.

    There are similar considerations with binary pulsars, of course.

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  53. Benjamin says:


    Calculating very roughly, I get a density of about 3 x 10^-13 kilograms per cubic metre (assuming the Pioneer spacecraft to be at 71 AU; assuming 90, you get about 2.3 x 10^-13). This is about five orders of magnitude more dense than your calculation would have it. Though I couldn’t find any data with more than one or two significant figures freely available, I was working mainly from press fact sheets, which is never very good and could easily have made the calculation meaningless.

    The real problem I see is that the two spacecraft are quite far apart, so you’d tend to have noticed the force being higher for the one further away. The difference would be smaller if the density of the dark matter halo decreases as you get further away from the sun.

    At least it should only show up at long distances, as the effect on the Earth would be tens of times smaller.

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  54. Lawrence B. Crowell says:

    Benjamin: I am not sure how you got that figure of 10^{-13}kg/m^3. That would be 10^{-10}g/m^3 or 10^{-16}g/cm^3. A proton at m ~ 10^{-27}g means a TeV DM particle is ~ 10^{-26}g, so your DM particles would be very hefty! I just worked directly with moles, which is easier IMO.

    Marshall: I agree that the gravitational effect of DM might be detectable in the solar system, even though it would be small. It is not clear to me that the Pioneer craft reflect this physics. That this anomaly is absent from the Voyager craft makes me suspect this is due to a leak or some differential cold gas to solid deposition or sublimation of atoms on the surfaces of the craft.

    Lawrence B. Crowell

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  55. Benjamin says:

    I did a rough calculation of what density would be required to produce the observed acceleration at a distance of 71 AU, which was the only figure I could find data for. It had nothing to do with the particles themselves.

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  56. Lawrence B. Crowell says:

    Ok, got you. I think this suggests that the Pioneer anomaly may not likely be due to DM. That is unless DM particles are very hefty, or much more abundant that one particle per “coffee cup.” We’d also have to sum this up over intergalactic volumes to see if this can reproduce the gravitational effects attributed to DM.

    Lawrence B. Crowell

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  57. Jason Dick says:

    The individual masses of the particles might not necessarily have to be that high, but they’d have to be quite clumpy, and I think that’s pretty much ruled out by our observation that dark matter tends to be vastly less clumpy than normal matter.

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  58. Lawrence B. Crowell says:

    The rational for DM as very weakly interacting with itself is that DM regions don’t exhibt much clumpiness. As far as I know the relative paucity of clumps is seen in the absence of localized Einstein lensing in DM regions.

    Lawrence B. Crowell

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  59. S Halayka says:

    Hi Sean,

    From what I understand, Matti Pitkanen’s work also directly discusses the possibilities of dark photons, dark chemistry, and dark biology.

    A brief Letter to the Editor, Foundations of Physics is at: http://cavekitty.ca/db_origin.pdf

    I’m hoping that they’ll publish it, since these are all very good ideas. I’d just hate to see Pitkanen’s hard work go unnoticed, etc, etc, etc.

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  60. MedallionOfFerret says:

    Since bridge sales are down a bit this month and bills are mounting up, would anyone be interested in purchasing one of several small dark worlds I happen to have on hand? Would be a great place to experiment with dark chemistry and dark biology. Be the first in your department to have one! String theorists are welcome–we speak branes fluctuationently. Wholesale prices, retail quality! (Shipping & handling extra)

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  61. Paul Murray says:

    ” Imagine there is a space with only one charge on it. Suppose the space is a sphere. Then in a classical picture the lines of force leave all these charges and have “nowhere to go.” ”

    Why is this not true of gravity?

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  62. Neil B ? says:

    I went to an interesting lecture at J-Lab today by Andrei Afanasev.


    “Search for Dark-Matter Particles in Photon-Photon Interaction at Optical Frequencies”

    He went over the basics of DM, including evidence from the Bullet Cluster (since approaching clumps of DM blew past each other and their formerly associated clumps of matter, I guess that close to rules out regular matter (RM) bases of DM such as MACHOs?) Andrei considers axions (of some sort) to be a good choice of what DM consists of, curiously not mentioned here. He discussed the LIPSS experiment, interesting to me as offbeat physics but also since I know and got to brainstorm with one of the main experimenters (K Beard.) I had already heard how hard it was to do right. Briefly: Take advantage of photon-photon coupling to produce some axions A or other DM particle by shining powerful laser through magnetic field. Stop conventional photons with a wall, and convert A back into photons with magnetic field on other side. It would be a tiny effect, much noise from cosmic rays, and the experiment turned out negative. That doesn’t mean “no DM can be produced from photon-photon reactions” but the mass must be even less (“milli-eV”)

    Another idea was directly relevant to “dark photons”, and that was the creation through the same means of what Andrei and some others call “paraphotons” which is presumably the same sort of idea. I told Andrei that should mean an equivalent para-charge analogy for the DM particles, which seemed odd to me and would maybe have prevented DM in the Bullet collision from cross-passing like that – he said, it weakly couples even to itself. He appreciates that we wouldn’t just have “four forces” in the universe any more.

    I forgot to bring up, that paracharged particles seem to imply an analogous “anti-dark matter” regime, and then the same question as for RM of why it didn’t all mutually disintegrate etc. (Also, they would be stable, not with 10^10 s half-life decay even into paraphotons, since paracharge presumably is conserved. BTW axions are thought to decay into ordinary photons.) There are other odd issues, like what role to virtual paraphotons play in the scheme of things? Maybe if virtual photons give the wrong vacuum energy level for DE, then VPPs do it right?

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  63. Neil B ? says:

    Update: The Afanasev talk slides are found at

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  64. Jason Dick says:


    Well, structure formation arguments basically rule out MACHO’s, as we see the evidence of dark matter even within the CMB, which was long before any compact objects had a chance to form. The Bullet Cluster does not, because MACHO’s are just as non-interacting as the stars and galaxies: they’re few and far between, so they mostly just miss one another in a collision like that.

    The difficulty with axions is that they have very low mass, which makes them a candidate for “warm” dark matter, which seems to not fit well with our current observations of structure formation. But, more observations are necessary to really say this with confidence, and perhaps the 21cm and cosmic shear observations will weigh in here to say something definitive.

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  65. Neil B says:

    (I hope this is OK to do, I got this “lost” comment from Sean using my browser cache of the old CV site):

    Sean on Nov 10th, 2008 at 12:32 pm

    Actually, axions are (usually) very much cold dark matter, not warm. It’s true that their masses are small — small enough to make them hot dark matter, if they were produced in thermal equilibrium. But they’re not; they come into existence at zero momentum as part of a Bose condensate. The energy per axion is enormously smaller than the energy per CMB photon.

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  66. Robert Bast says:

    A discussion on this topic, although I named it “anti-light”, is at my forum:

    Something you may want to consider is how fast a dark photon travels….

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  67. Neil B says:

    Robert, if anti-light traveled at 10c as you suggest, it would make causality troubles in our universe if it could ever be detected (read about special theory of relativity.) However, such alternate photons might go slower than our light.

    Also, “dark photons” as imagined by Sean and others are not like negative energy that can cancel out ordinary light or energy, they are “dark” because we can’t see them (i.e., they don’t interact with ordinary matter-energy enough.)

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  68. Lawrence Crowell says:

    Negative energy is of course unlikely. In this case the eigen-numbers or spectrum of quantum field theory is not bounded below. This has serious pathological consequences.

    L. C.

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  69. Jason Dick says:

    Neil B,

    Interesting. Guess that shows that I haven’t been following axions very closely.

    Robert Bast,

    Anti-light is a really bad name. It can only cause confusion as it evokes anti-matter, which is a completely different phenomenon. In fact, there is an anti-particle to the photon: it’s called the photon (so yes, this means that just as an electron and a positron can annihilate with one another to produce all sorts of things, a photon can annihilate with another photon, if the pair have enough energy between them to produce anything).

    I honestly don’t see how the speed of dark photons could be any different from normal photons unless they have some mass, which would cause the force to be short range, which would be something other than what Sean is proposing.

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  70. Hoseki says:

    This guy, Jay Alfred, has written a lot about “dark plasma” since 2006 in his books. He argues in his article “Dark Matter – Plasma of Super Particles” (June 2008) that “…dark matter consists of non-standard (or super) plasma which radiates energetic waves. These postulated “super” waves or “S-Waves” are currently not directly measurable by our scientific instruments.” See http://ezinearticles.com/?Dark-Matter—Plasma-of-Super-Particles&id=1240357.

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  71. Hoseki says:

    Sean, I’m trying to understand what you said: “Yes, I forgot to mention: our DM candidate is certainly not some superpartner of any of the particles in the Standard Model, since we don’t want any of them to carry dark charge.”

    Did you not argue in your paper that the DM candidate could be a WIMP (which is a linear combination of super partners)? Furthermore, it is stated in your paper that the particles have a dark U(1) charge (but there is overall charge neutrality). Puzzled…

    By the way the link to Jay Alfred’s article should be:


    (without the full-stop at the end … hope it works this time)

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  72. Ray Gedaly says:

    Brane Matter … Could dark matter be evidence for parallel branes? Matter in our brane and other(s) would only interact via the gravitational force.

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