Thursday, March 27, 2014

A new cosmological coincidence problem?

One of the consequences of the BICEP2 data from last week, should it hold up to scrutiny, and be seen by other experiments (I hope it holds up to scrutiny and is seen by other experiments), is that there is a significant lack of "power" in the temperature anisotropies on large angular scales.

What that sentence means is that when you look at the CMB in very large patches on the sky (about the size of the moon and bigger) its temperature fluctuates from patch to patch less than we would expect.

This was already somewhat the case before the BICEP2 discovery, but BICEP2 made it much more significant. The reason for this will hopefully turn into a post of its own one day, but, essentially, the primordial gravitational waves that BICEP2 has hopefully discovered would themselves have seeded temperature anisotropies on these large angular scales. Previously, we could just assume that the primordial gravitational waves had a really small amplitude and thus didn't affect the temperature much at all. Now, however, it seems like they might be quite large and therefore, this apparent lack of power becomes much more pertinent.

That's all fine and is something that any model of inflation that hopes to explain the origin of these gravitational waves will need to explain, despite what many cosmologists already writing papers on the ArXiv seem to want to believe (links withheld). As a side, ever-so-slightly-frustrated, note, the only papers I've seen that have actually analysed the data, rather than repeating old claims, have confirmed this problem that was clear from, at the latest, the day after the announcement.

But why does it imply a "cosmological coincidence problem"? And why is it a new coincidence problem? What's the old one?

The old cosmological coincidence problem

The energy density attributable to a  cosmological constant is, well, constant. The energy density of matter and radiation drops as the universe expands. Right now, today, the energy densities of matter and of "dark energy"/the cosmological constant appear to be similar. If we extrapolate into the distant future, almost all of the energy density of the universe will be dark energy and in the past almost none of it was.

The first cosmological coincidence problem is that we live and observe at precisely the time of this transition. That is supposed to seem a bit odd. When I'm in the right mind, I agree. There are a number of possible explanations for it, most of them anthropic (though some aren't - e.g. if dark energy is related to structure formation).

This is a problem well-known amongst cosmologists and something often pondered about.

The new cosmological coincidence problem(s?)

However BICEP2 suggests a new one. The universe is expanding. But light also travels at a finite speed. Therefore, as time goes on more of the universe becomes visible to us (at least so far) as we see farther and farther away. The result of this is that the largest angular scales we can currently see (the patches on the sky bigger than the moon) have only "recently" become visible. If we were around when the CMB formed, we would observe a much smaller fraction of the currently observable universe.

Maybe you're starting to see where the new coincidence problem comes from. The behaviour of the universe on all the angular scales smaller than the moon appears to be consistent and well described by one model, whereas the fluctuations on the largest angular scales appear to follow a different model.

Why do we observe this transition today?

If we were around billions of years ago we wouldn't even know that this funny behaviour had occurred, because these very large distance scales would still be "outside our horizon", we simply wouldn't be able to see them because light couldn't have brought us knowledge of them yet.

So, the new cosmological coincidence problem is that this strange behaviour is becoming visible to the universe at precisely the same time as we are here observing it. Why now (if it has to happen at all) and not much later or much earlier?

Is a potential explanation again anthropic? Did the universe need to have some minimum size in order for intelligent life to have enough time/space to evolve and we're now seeing the edge of our homogeneous, observable, patch? Whereas, in other, smaller (and more common?), patches there is no life to see this effect happen much earlier?

As a final comment, I can't help but think that there is then an obvious third coincidence problem that arises when you combine both of the others. If it is a strange coincidence that we are around just as dark energy comes to dominate the universe and it is a strange coincidence that we are around just as this funny feature in the primordial fluctuations of the universe becomes visible, then it is also a strange coincidence that dark energy comes to dominate at exactly the same time as the primordial fluctuations change their shape.

Is it all anthropic? Is the same physical mechanism that is responsible for dark energy also responsible for these large scale features? Have I just lost any chance of getting a permanent job in serious cosmology? Time will tell (at least I didn't put it on the ArXiv!)

Twitter: @just_shaun


  1. Interesting thoughts, and I doubt they'd jeopardize your job prospects. I just wanted to point out two things for the benefit of your readers (you obviously know them already).

    The first is that anthropic "solutions" to the first coincidence problem - scare quotes because they haven't yet solved anything - also relate dark energy to structure formation, just via a different argument. The second is that when you say "the behaviour of the universe on scales smaller than the moon", you probably mean "on scales smaller than the scales which, at the distance of the last scattering surface from us, would subtend angles on the sky smaller than that subtended by the moon".

    1. Ah, yes, thanks for that. I was missing the word "angular" in that sentence.

      I think your first point is a bit pedantic though. The anthropic "solutions" (I accept the requirement of scare quotes) don't claim that dark energy is *caused* by structure formation, only that in a universe with sentient life the vacuum energy must be small enough to allow structures to form. The other solutions I was alluding to (i.e. backreaction) actually claim that the phenomena we measure and attribute to dark energy are a direct result of the formation of structures.

  2. "If we extrapolate into the distant future, almost almost all of the energy density of the universe will be dark energy and in the past almost none of it was." This is an interesting conjecture. Note that in my quantum theory of gravity the % of dark energy is a constant (roughly 72.8 % over cosmological time). According to Linde and Guth it is merely a coincidence that (1 - .728)/.728 = (approx) 3/8 but in my theory it is because string vibrations are confined to 3 copies of the Leech lattice. On the basis of overwhelming empirical evidence, Milgrom is the Kepler of contemporary cosmology. Is the preceding statement wrong? Note that Kroupa is scheduled to give a talk at the IAS on Thurs., 24 April 2014.
    Astrophysics Events, School of Natural Sciences, IAS

  3. Can one have it both ways? If one number is much smaller than another, then some see this as a problem. Why is the cosmological constant so small? If one number is about the same as another number, then some see this as a coincidence problem.

    Shouldn't just one of these be a problem?

    My vote is for near equality. If two numbers have essentially nothing to do with each other, chances are that their ratio will be large. If they are similar, there is probably a reason. It seems to me that a weak-anthropic (the dash is crucial) solution to the coincidence problem is completely adequate.

    What do you think of ?

    1. I don't think it is having it both ways.

      For the coincidence type problem, if two numbers that shouldn't a priori have anything to do with each other end up being very close to each other, then this is suspicious and seems to imply that the two numbers might be related by a more fundamental theory.

      For the "too small" type problem, if our fundamental theories say that a measurable number should have a natural, or generic, or most likely size and it is measured to be many orders of magnitude smaller then this implies something is cancelling against the prediction, or dynamically reducing it, or that for some other reason large values of this number aren't allowed by nature due to some new symmetry/force/physics we haven't yet discovered.

      If one number is much smaller than another number, but we have no a priori reason to expect those numbers to be related then that wouldn't be seen as a problem.

      I hadn't read that paper before. I think it is fair to say (as they do) that a geometrical cosmological constant has no a priori expected value and thus could be anything, including what me measure today and that therefore "dark energy" is not mysterious or unexplained. We in fact have a very good a priori model that explains all phenomena currently attributed to dark energy perfectly fine. The question is then on quantum field theory to explain why its prediction is so wrong. I would agree that this problem exists whether \Lambda is zero or non-zero, but it is still a problem. And it seems reasonable to hope that any explanation of why the QFT vacuum energy is so small might also predict the precise value of the measured cosmological constant. But I do find modified gravity/quintessence models less compelling as explanations of \Lambda for exactly this reason, they don't solve the QT problem and a cosmological constant is already a perfectly adequate explanation of everything else about dark energy.

    2. But this is also why I find the anthropic multiverse explanation of \Lambda at least a little compelling because, if it works, it *does* solve the QFT problem at the same time as "predicting"-ish the amplitude of the cosmological constant.

  4. That isn't a prediction really is it. But I agree that AP is not useless. But science is more than philosophy. Just explaining not enough. If it had been, then that's what they all would done in centuries gone by. It's lot easier to come up with some generic explanation than nail an aspect of nature down hard, which takes a persons whole life. If they had been settling for multiverse explanations - and they might because the multiverse could have been proposed for any of the big challenges. If they had done that, there would be no such as science. It would never have happened. And if we accept the multiverse and AP and the other infinity-dependent explanations, that's what it'll be in 200 years or 1000 years. Science dies. Because scientists lose their scientific worldsense....they forgot or never learn what is expected of an inventor and pioneer in SCIENCE. And then they give jobs to other mediocre people, and 30 years later we have what we have now. A physics community less bright than the dentistry and general medical examiner communities. On a par with solicitors. And that is not enough.