Dark Energy: Still a Puzzle

The arrow of time wasn’t the only big science problem garnering media attention last week: there was also a claim that dark energy doesn’t exist. See Space.com (really just a press release), USA Today, and a bizarre op-ed in the Telegraph saying that maybe this means global warming isn’t real either, so there.

The reports are referring to a paper by mathematicians Blake Temple and Joel Smoller, which is behind a paywall at PNAS but publicly available on the arxiv. (And folks wonder why journals are dying.) Now, some of my best friends are mathematicians, and in this paper they do the kind of thing that mathematicians are trained to do: they solve some equations. In particular, they solve Einstein’s equation of general relativity, for the particular case of a giant spherical “wave” in the universe. So instead of a universe that looks basically the same (on large scales) throughout space, they consider a universe with a special point, so that the density changes as you move away from that point.

Then — here’s the important part — they put the Earth right at that point, or close enough. And then they say, “Hey! In a universe like that, if we look at how fast distant galaxies and supernovae are receding from us, we can fit the data without any dark energy!” That is, they can cook up a result for distance vs. redshift in this model that looks like it would in a smooth model with dark energy, even though there’s nothing but ordinary (and dark) matter in their cosmology.

There are three things to note about this result. First, it’s already known; see e.g. Kolb, Marra, and Matarrese, or Clifton, Ferreira, and Land. In fact, I would argue that it’s kind of obvious. When we observe distant galaxies, we don’t see the full three dimensions of space at every moment in time; we can only look back along our own light cone. If the universe isn’t homogeneous, but is only spherically symmetric around our location, I can arrange the velocities of galaxies along that past light cone to do whatever I want. We could have them spell out “Cosmic Variance” in Morse code if we so desired. So it’s not very surprising we could reconstruct the observed distance vs. redshift curve of an accelerating universe; you don’t have to solve Einstein’s equation to do that.

Second, do you really want to put us right at the center of the universe? That’s hard to rule out on the basis of data — although people are working on it. So it’s definitely a possibility to keep in mind. But it seems a bit of a backwards step from Copernicus and all that. Most of us would like to save this as a move of last resort, at least while there are alternatives available.

Third, there are perfectly decent alternatives available! Namely, dark energy, and in particular the cosmological constant. This idea not only fits the data from supernovae concerning the distance vs. redshift relation, but a bunch of other data as well (cosmic microwave background, cluster abundances, baryon acoustic oscillations, etc.), which this new paper doesn’t bother with. People should not be afraid of dark energy. Remember that the problem with the cosmological constant isn’t that it’s mysterious and ill-motivated — it’s that it’s too small! The naive theoretical prediction is larger than what’s required by observation by a factor of 10120. That’s a puzzle, no doubt, but setting it equal to zero doesn’t make the puzzle go away — then it’s smaller than the theoretical prediction by a factor of infinity.

The cosmological constant should exist, and it fits the data. It might not be the right answer, and we should certainly keep looking for alternatives. But my money is on Λ.

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55 Responses to Dark Energy: Still a Puzzle

  1. LBBP says:

    “Second, do you really want to put us right at the center of the universe?”

    Well, this sure would make a lot of Catholics happy.

  2. martin g says:

    That’s right ‘ dark energy ‘ doesn’t exist. Neither does ‘ dark matter ‘.

    My reasoning revolves around a simple question : viz. ‘ Where is it ? ’

    For it’s certainly not around our bit of the universe. If it was, then all our calculations about how local astronomical objects ( and very local ones here on earth ) would be out by a factor of about 90% or so.

    But every ( local ) observation matches more or less exactly with our traditional Newtonian and Einstein-ian calculations.

    So there’s no ‘ dark anything ’ around here. If there was then, say, launching a satellite would be a very problematic exercise.

    But it would be very weird indeed if our part of the universe was specifically excluded from all this ‘ dark stuff ‘ that is alleged to pervade the entire universe.

    There’s something peculiar going on of course ( with the observations of distant galaxies etc ) but ‘ dark-ness ‘ isn’t the answer. More likely an as yet unknown phenomenon acting only at very large distances – or variable light speed / gravity etc etc .

    Forcing the math to fit – with the invention of 90% or so invisible material and force – seems to me to be a gargantuan ‘ dark fudge ‘.

  3. Fermi-Walker Public Transport says:

    The real reason for “putting us at the center of the universe” is to bring back epicycles.

  4. Joseph Smidt says:

    “This idea not only fits the data from supernovae concerning the distance vs. redshift relation, but a bunch of other data as well (cosmic microwave background, cluster abundances, baryon acoustic oscillations, etc.), which this new paper doesn’t bother with.”

    For me this is the sticking point. I keep hearing “this explains this and that explains that”, but there seems to be only one theory that explains them all in a very straight forward way: Dark Energy.

  5. miller says:

    I am curious, what is the naive theoretical prediction of the cosmological constant? How is it made?

    Also, I would like to see upper bound error bars on our distance to the center of the universe.

  6. tacitus says:

    My reasoning revolves around a simple question : viz. ‘ Where is it ? ’

    For it’s certainly not around our bit of the universe. If it was, then all our calculations about how local astronomical objects ( and very local ones here on earth ) would be out by a factor of about 90% or so.

    I am no expert, but if this was as glaring a problem as you seem to think it is, then dark matter/energy would have been dismissed as a solution years ago. Astronomers may be puzzled, but they aren’t dumb.

  7. noname says:

    At tacitus (6) and martin g (2)-

    The universe is about 5% ordinary matter, 20% or so dark matter, and 75% or so dark energy. This is the percentages you get when you add over all mass and energy in the universe.

    Ordinary matter, however, tends to form very tight clumps, like stars, while dark energy clumps only on much larger scales. Dark energy is even more extended, being uniformly or almost uniformly spread accross the entire universe.

    So- if you look at something like our solar system, almost all the mass and energy in it is comprised of ordinary matter. The density of the dark matter and dark energy is so small, than in the tiny volume compised by our solar system you don’t find very much of it all- all the mass is contained in the tight clump formed of ordinary matter that we call the Sun.

    If you now ask about the matter distribution in a much larger piece of the universe, like our galaxy, you will find that both ordinary matter and dark matter are important, and consitute comparable fractions of the total energy budget (which one is bigger depends on where exactly you decide to draw the “edge” of our galaxy). Even on galactic scales, however, the density of dark energy is low enough that the amount of dark energy contained in a galaxy is very small.

    It is only once you add over the entire volume of the universe that dark energy becomes the dominant form of energy. This happens because ordinary matter and dark matter forms tight clumps (i.e. galaxies) that are separated by VERY large amounts of space that have dark energy, so even though the dark energy density is small, once you add over all that space in between galaxies, the net amount of dark energy over a given volume ends up being larger than that or dark matter or dark energy.

    So, to summarize: the amount of dark matter and dark energy in our solar system is negligible compared to the amount of ordinary matter, and therefore all we need to keep track to understand the behaviour of planets and satellites in our solar system is the ordinary matter.

  8. LBBP, most modern geocentrism is from Protestants not Catholics.

  9. MickelsonMorley says:

    The dark energy/matter debate keeps reminding me of the debate about the ether (medium for light). Scientists couldn’t fathom a world in which there was no medium for light to travel through … then these two guys proved there was no ether (medium) … I can’t remember their names …. Anyway, that discovery seems to have kinda, I mean, you know, completely changed humanities understanding of physics … no? Maybe that’s what will happen with Dark matter/energy?

  10. Martin g says:

    The ‘ dark matter ‘ which inhabits the vast intergalactic voids must be even more unusual than I thought. Considering how massive it is and how much of it there is, it seems odd that it’s immune to, say, the gravity of our Sun – or indeed our entire Galaxy. Why hasn’t some of it been attracted here ? It’s had a few billion years to condense. But the most noticeable thing about it is its absence.

    The ‘ Emperor’s New Matter ‘ I reckon.

  11. Kernal says:

    @Martin g
    Since dark matter interacts so rarely, a particle with some angular momentum will never lose that angular momentum, preventing it from being able to condense into the Sun. Regular matter doesn’t have this problem, so it does fall into gravitational wells and form stars, planets, etc.

    Regarding your earlier point about lacking evidence, DAMA has claimed a direct detection of the stuff.


  12. Mark says:

    I’d advise against feeding the trolls.

  13. jpd says:

    saying everyone is at the center of the universe no matter where they are is as
    crazy as saying everyone measures the same speed of light no matter how they
    are moving.

  14. Matt says:

    I’m just curious what happens if every point is the center of the universe, mathematically speaking?

  15. jpd says:

    its a big boost for my ego.

  16. Albert Bakker says:

    #7 noname and others, I don’t share the DM scepticism of Martin G (#2) but his logical reasoning on the surface seems sound that if DM interacts gravitationally identically to baryonic matter, then given sufficient naivety, it seems inescapable to conclude that if baryonic matter clumps together in denser regions of space that DM would also. And therefore if that would be the case, ignorant of it’s existence, we would just have assumed gravity to be a stronger force. Or in other words we would have measured a bigger value for G.

    Just stating however that it isn’t so because dark matter clumps on larger scales, even if it is true, isn’t really a statisfying answer.

    I have the same naive concern with why DM remains so smoothly distributed, but I have no trouble postponing the demand for an answer until I can claim my ignorance to be no longer complete.

    But the question has been asked before and some ideas were offered in response, like for example the kinetic energy collapsing cold DM particles would gain falling in would then be unable to dissipate by emitting radiation because the particle can’t emit photons and so perhaps pressure would rise much too quick, resisting further collapse.


    (The question is asked in comment 16 followed by attempts at answering this question.)

  17. Aaron Sheldon says:

    huh did I miss something? They make the claim that the truncated perturbation of the FWR metric solved the Einstein equation for the standard p=rho c^2 / /3 condition, but I did not see an explicit calculation of the stress-energy tensor anywhere in the paper. I think that would have been the least minimal ‘oh yeah, prove it’ sort of thing a reviewer would ask for.

  18. noname says:

    Hi Albert.

    You are right that there is indeed a deeper truth concerning my original response, and you are also right as to why dark matter does not collapse into tight clumps like stars.

    Dark matter does not collapse into tight clumps because it is dissipationless. That means that as dark matter particles fall into the galaxy, they start moving faster and faster. For them to fall into a tight clump like a star, they would need to find a way of loosing this extra energy. For normal matter, this is not a problem: it looses energy by emitting light. Dark matter, on the other hand, can’t emit light, and therefore does not have a way to slow down.

    So what happens to the dark matter then? Well, it falls towards dense regions (like galaxies), but since it can’t get rid of their extra energy, it ends up forming a “gas” of dark matter particles around the galaxy, in which there is a nice balance between the pull of the galaxy (including the gravity from the dark matter particles), and the velocity of the dark matter particles. We call this “gas” of dark matter particles the halo of the galaxy, and the balance between the velocity of the particles and how far they extend (which is related to how strongly the particles are pulled) is called “virial equilibrium”.

    The dark matter halo of a galaxy typically extends out to much larger radii than the stars, so much so that in the region of space where we can actually find stars (what we usually call the galaxy), there is typically more regular matter than dark matter. It is only when you go out to much larger radii and include all the dark matter in the dark matter halo that you discover that the matter around a galaxy is comprised mostly of dark matter. If you pick a small volume such as a Solar System sized chucnk around a star such as our Sun, the total matter in the Sun completely overwhelms the relatively small amount of dark matter in that piece of sky.

    So, in short, the dark matter doesn’t form tight clumps like stars because, as it falls, it gains velocity, and has no way of getting rid of this extra energy. Instead, the dark matter ends up forms extended halos around galaxies that reach out to much larger distances than the stars in the galaxy.

    One things that is worth noting is that in the evolution of the universe, it is actually the dark matter halos that form first. That is, because most of the matter in the universe is dark matter, the dark matter start coallescing and forming these extended clumps that we call the halos. Then, the regular matter that is in these halos starts loosing energy (e.g. by emitting light), condensing into the middle of the halos. There, it starts forming stars, and that is what we end up seeing as galaxies, with the dark matter halo in which the galaxy forms being much larger than the galaxy itself.

    Hopefully this is a more satisfying answer. 🙂

  19. Albert Bakker says:

    Thank you noname (#19) for spelling it out and making it so clear. That was a satisfying answer indeed. Thanks!

  20. DG says:


    No wonder my Cavendish experiment setup in Senior Lab produced such poor results: I did it with the lights on!

  21. Just Learning says:

  22. BlackGriffen says:

    Speaking of spelling “Cosmic Variance” in the stars, there’s a potentially fun and challenging simulation project you could do with that. Make software that searches for a position in the present configuration of stars that makes a constellation of the desired shape. Even better, but more challenging, is to allow it to search time as well (ie simulate the motion of the stars).

    Once you’ve done that, have the tool search for an image of Jesus or Mary or whatever and then, hey bingo, manned space flight will have all the budget it needs from the religious lot because they’ll want to get out there and see “space Jesus.”

  23. Arrow says:

    The fact that we have no idea what 90+% of the Universe is made of is a clear indicator that something is *very* wrong with our fundamental physics.

  24. Brian137 says:

    “Second, do you really want to put us right at the center of the universe?”

    Forget the “us.” Y’all seem to be forever approaching and receding, approaching and receding, mostly obliquely.

  25. Pope Maledict XVI says:

    Who publishes in PNAS anyway? Apart from publicity hounds.