Preposterous Universe

Wednesday, March 30, 2005
Friedmann fights back

For those of you interested in the attempt by Kolb, Matarrese, Notari, and Riotto to do away with dark energy, some enterprising young cosmologists (not me, I'm too old to move that quickly) have cranked through the equations and come out defending the conventional wisdom. Three papers in particular seem interesting:
  • Éanna Flanagan, hep-th/0503202
    "Can superhorizon perturbations drive the acceleration of the Universe?"
  • Christopher Hirata and Uros Seljak, astro-ph/0503582
    "Can superhorizon cosmological perturbations explain the acceleration of the universe?"
  • Ghazal Geshnizjani, Daniel Chung, and Niayesh Afshordi, astro-ph/0503553
    "Do large-scale inhomogeneities explain away dark energy?"
I think the general lesson seems basically in line with my earlier suspicions. (Not that I'm claiming any sort of priority; the people who do the work should get the credit.) I mentioned the idea of the vacuole models, which give you exact solutions for large-scale perturbations without any spatial gradients. In that case you recover precisely the ordinary Friedmann equation governing cosmological evolution, just with a set of cosmological parameters that differ from the background values. Of course this isn't the end of the story, because in general perturbations will have spatial gradients, even if they are expected to be small for very long-wavelength modes. If they're not small, they should probably show up in other ways -- as spatial curvature, or as large-scale anisotropies.

The new papers seem to demonstrate that this is indeed the case. (See also comments by Jacques and Lubošš.) You can use a GR trick (the Raychaudhuri equation) to define what is basically the "locally measured Hubble constant and deceleration parameter," and relate them to the locally measured energy density and pressure, as well as the "shear" and "vorticity" of the fluid filling the universe. The important thing, of course, is that everything is defined at each tiny region of spacetime, without appealing to what is happening far away. For a perfectly homogeneous and isotropic universe, the shear and vorticity vanish, and you recover the ordinary Friedmann equation (that's the lesson of the vacuole models). Perturbations with spatial gradients will generically induce both shear (stretching) and vorticity (twisting) of the fluid, and these can indeed lead to deviations from the Friedmann relation. But the effect of shear is always to make the universe decelerate even faster, not to make it accelerate. Vorticity can lead to acceleration, but it is usually small; indeed (as mentioned by Hirata and Seljak), in the KMNR set-up the vorticity is zero all along. So there can't be any acceleration. In fact Hirata and Seljak claim to have found exactly where the higher-order perturbative analysis of KMNR went astray; I haven't checked it myself, but they're most likely right.

You will have noticed, of course, that there weren't very many days in between the appearance of the original paper and the appearance of various refutations. I can imagine what these folks all went through, working diligently through the weekend. I did that myself once, when a misleading paper (much much worse than KMNR) was getting a lot of attention and needed to be set straight, but I'm glad it's not my standard operating procedure.

What would be really nice, even if the ultimate consensus settles down to a judgment that KMNR weren't right, is if people understood that this is the way science works. Individual papers may be right or wrong; but they are put out there for the community to debate about, different critiques are put forward, and eventually the truth comes out. Everyone is after the same thing, trying to figure out how the universe works. Something our creationist friends will never quite appreciate.

Ideas on culture, science, politics.
Sean Carroll

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