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Low-functioning pinhead...
March 30, 2005
BF
While we’re on a cosmological constant kick, I should mention a recent paper by Stephon Alexander. He claims to have found a mechanism by which the cosmological constant can be relaxed to a small value.
Which sounds pretty important. Anyone who’s been in the field for any length of time has tried and failed to find such a mechanism.
It’s well known that four-dimensional gravity has a CP-violating topological term,
which is very analogous to the -term in QCD. If you have a Dirac fermion, chiral rotations are anomalous in a curved space background. A massless fermion makes the -angle physically unobservable. If the fermion has a mass, then the linear combination
is observable. In QCD, the apparent smallness of is a problem, and the Peccei-Quinn mechanism was invented to solve it. is replaced by a pseudoscalar field, the axion. Chiral symmetry breaking induces a potential for the axion which causes it to relax to zero.
Stephon points out that a very similar mechanism can be made to work in gravity, relaxing the gravitational -angle.
“Who cares?” I hear you cry, “Gravity is so weak, gravitationally-induced CP-violating effects are unmeasurably small. Besides, I thought you were going to tell us about the cosmological constant.”
March 29, 2005
Sweetness
I sat down last night, with my two children, to watch the much-protested “Sugartime” episode of Postcards from Buster. A sweet, wholesome half-hour tour of life in rural Vermont (as seen through the video camera of the eponymous rabbit). Lots of maple sugar, dairy cows, and even a Shabbos dinner. Having now seen the show, I am more amazed than ever at the “controversy” it engendered.
We have a contingent of seriously twisted people in this country. And I don’t mean “Mom and Gillian,” the parents of Buster’s tour guides in this episode.
March 28, 2005
Superhorizon Fluctuations and Dark Energy?
There’s been a lot of buzz about Kolb et al’s suggestion that superhorizon fluctuations can mock-up the effect of a cosmological constant (current observations suggest ). I haven’t commented, because the calculations are a bit beyond me. They involve intricacies of second-order perturbation theory about FRW, and an infrared divergence which implies that — even though the amplitude of fluctuations at any individual wavelength is small, — if there have been enough e-foldings of inflation, the contributions from all superhorizon modes may be large enough to actually dominate the energy density today.
Éanna Flanagan has a very interesting critique, which is simple enough that even I have a chance of understanding it.
Consider a gedanken-universe in which the initial spectrum of perturbations was such that there are no sub-horizon perturbations today. An observer in such a universe can measure the redshift, and luminosity distance, of nearby events. In a conventional FRW universe, these are related by
But, since we won’t assume local isotropy, we have some more general angle-dependent relation,
and one reconstructs and as some angular averages of and . The cosmological fluid has a stress tensor, . One can expand the four-velocity in the usual way,
where , , and are the expansion, shear, vorticity and four-acceleration. Assuming matter domination and no dark energy, and hence implies .
At this point, Flanagan uses a local Taylor series expansion to compute and in terms of the density and the four-velocity and its gradients. The result is that the Hubble constant
measures the local expansion of the fluid and the deceleration parameter,
The first term is positive. In a spatially-flat, matter-dominated FRW universe, we would have