Preposterous Universe

Tuesday, March 22, 2005
Doing away with dark energy?

The universe is accelerating, and we don't know why. The most straightforward explanations involve dark energy -- some source of energy that is spread smoothly throughout space, and whose density constant (or nearly so) as the universe expands. But there are problems with the dark energy idea, especially in its magnitude; a back-of-the-envelope calculation says that the amount of energy in the vacuum should be larger than what we observe by a factor of about 10120. Inexcusable, even by cosmology standards.

So we might try to be even more dramatic -- maybe Einstein was wrong, and we have to modify general relativity on cosmological scales. But of course we should keep in mind the possibility of less dramatic resolutions; maybe an explanation for the acceleration of the universe can be found in the context of conventional physics, without invoking dark energy at all. That's the hope expressed in a recent paper by Kolb, Matarrese, Notari, and Riotto (KMNR).

The paper has already garnered some attention -- here's the press release, and a note at Peter's blog. And it's reached the media, albeit with some skeptical notes: here's an article that quotes Michael Turner, and here's one that quotes me. (Poor Rocky hasn't even convinced his Chicago colleagues!)

Why the skepticism? My original notion was not to comment in any detail until I actually understood the paper better. But then I remembered -- this is a blog. Withholding comment until I understood what was going on would be unbloggy of me.

So, even though I certainly haven't gone through their equations, the basic idea seems to be clear. We often talk about the fact that our universe is very smooth (homogeneous and isotropic) on large scales, but of course it isn't perfectly smooth. There are slight differences in the density of matter from place to place, even when we average over huge distances. It is convenient to think of the actual deviation of the density from its background value as arising from a sum of many contributions, each taking the form of a sine wave with some specific wavelength and amplitude; we can then describe the effects of each of these modes independently. These perturbations are thought to originate in the early universe, and are responsible for the existence of galaxies and clusters today.

The KMNR idea is simply this: there is some fluctuation mode with a wavelength that is much larger than the radius of our currently observable universe, that also has a large amplitude. The effect of this mode is to alter the relationship between our conventional cosmological parameters, such as the mass density and the expansion rate. In particular, it is possible to find realizations (so the claim goes) in which we would observe our local patch of universe to be accelerating, even if there weren't any dark energy.

The derivation of this result involves a lot of math. But it should be possible to understand the reason why people are skeptical. In general relativity, no influence can travel faster than the speed of light. Since there is only a finite time since the Big Bang (14 billion years), there is only a finite piece of universe that possibly could affect what we see today. (The observable universe actually has a radius of about 46 billion light years, not 14 billion light years, because of sneaky expansion effects.)

Now, it's certainly possible for some perturbation with a wavelength much larger than our observable universe to have an effect on us, but the effect only comes from the piece of that perturbation that is inside our patch. KMNR claim that the effect is to change the relationship between the observable cosmological parameters (such as the density, spatial curvature, expansion rate, etc.). I find it hard to believe. My hunch is that such a perturbation should change the values of the parameters, but they should keep the same relationships that they had before. For example, if we measure the density and the curvature of space, conventional cosmology tells us that we can figure out the expansion rate using the Friedmann equation. I think that an ultra-long-wavelength perturbation will shift the values of the density/curvature/expansion from their values in the unperturbed background, but will do so in a way to preserve the Friedmann equation. KMNR claim otherwise.

Even though I haven't gone through their math, I do have some evidence on my side. A long time ago cosmologists developed the "vacuole" models as ways to understand cosmological perturbations. (See e.g. this paper paper by Hammer.) To make a vacuole, start with a spherical region of a perfectly uniform universe. Now take the matter inside your spherical region and squeeze it a little, rearranging it into a smaller uniform spherical distribution with a higher density. There will be a region in between your overdense sphere and the external universe that is completely empty. It turns out that you can solve Einstein's equation exactly for this situation. The outside universe acts completely conventionally with whatever cosmological parameters it had to start, unaffected by your rearrangement. The empty thick shell you have created will be the Schwarzschild solution, since Birkhoff's theorem says that any spherically symmetric vacuum solution to Einstein's equation is Schwarzschild. And the interior region will behave exactly like a homogeneous and isotropic universe in its own right, except with different values of the cosmological parameters. These parameters will exactly obey the conventional Friedmann equation, and someone who lived inside there would have no way of telling that those parameters didn't describe the entire universe.

This is by no means a proof that KMNR are wrong; the vacuole model describes one very specific type of perturbation, and it may be that only other kinds of perturbation give their effect. But before I buy into it, I would need to understand better how local physics inside my observable patch can violate the conventional Friedmann equation. The good thing about science is that there is a right answer; in the case of the accelerating universe, it's well worth exploring all possible avenues to getting it.

Ideas on culture, science, politics.
Sean Carroll

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