Sunday, May 28, 2006

Steinhardt and Turok: cyclic model and cosmological constant

Paul Steinhardt and Neil Turok propose their solution of the cosmological constant problem

based on the cyclic model. See also the Science magazine. What is their key idea? The full age of the Universe is not the usual 13.7 billion years but much more: exponentially more. The boring de Sitter eras take a lot of time, but the Universe always eventually collapses and starts a new life cycle. During this process, the value of the cosmological constant may be reduced: imagine the cosmological constant to be the potential energy of a complicated axion field.

This picture differs from the anthropic explanation because in their model, if you imagine that someone makes it truly well-defined (or even embedded in string theory), the cosmological constant is essentially a function of the total time since the beginning of the Universe. Because the relaxation time gets longer as the cosmological constant approaches zero, most of the time is spent in regions with a small cosmological constant. The small value is generic - unlike the anthropic picture where the small values are rare.

Although their explanations why the vacuum energy is small may look statistical, chaotic, and similar to the anthropic reasoning to us, the previous paragraph makes a lot of difference. They voice my usual counter-argument against the anthropic reasoning using rather clear and convincing words:

• All other things being equal, a theory that predicts that life can exist almost everywhere is overwhelmingly preferred by Bayesian analysis (or common sense) over a theory that predicts it can exists almost nowhere.
Yes, I would prefer to call it "common sense" although it is fair to say that this common sense is related to the Bayesian analysis. But the argument is more important. If your (anthropic) theory predicts that what we observe (life) is extremely unlikely and rare, it is always inferior in comparison with a theory that predicts that things we see are generic. Good theories are those that make the predicted numbers - and probabilities - closer to the observed ones - or more likely - than expected a priori. The anthropic explanations don't offer any improvement of this sort.

In their rough calculation, the small cosmological constant is indeed more "generic". One can get a similar positive discrimination for small positive values of the cosmological constant as one obtains in the Hartle-Hawking wavefunction. This could of course lead to a similar problem: why is not the cosmological constant exactly zero which might be more likely than the observed finite value?