The Quantum Structure of Space and Time (293 pages)

Cosmology 265

the potential is technically natural. But, this is a new idea; you could think

of lots of different kinds of potentials that may be more appealing; you might

consider different kinds of time histories in which you could use the same basic

principles of ”ultra-slow relaxation” and cyclic evolution. There may be even

better ideas out there.

H. Nicolai I have a question to Steinhardt. How do you reconcile the second law

of thermodynamics with the cyclic universe?
P. Steinhardt Essentially what happens in this model is that at each stage when
you have a collision, you produce a lot of entropy. Then during the subsequent
stages of expansion you stretch the branes and you spread the entropy out so
that the entropy density becomes exponentially low. And then you have another
collision which creates more entropy. So, entropy is actually building up, if you
add it up over the entire brane from cycle to cycle. But the entropy density is
cycling, and it is the entropy density that is important for cosmology, for an
observer like us who can only observe within the horizon. So the entropy is out
there, it is just too spread out for us to see it.

F. Wilczek First I would like to say something profound, and then I will illustrate

it with something which may or may not be profound. The profound thing I

would like to say is that it is sometimes possible to solve some problems without

solving all problems. I would like to illustrate that with the case of axion

cosmology which was alluded to here. In that case, the assumptions leading

to a kind of multi-verse picture, namely what ordinarily might be thought of

as universal parameters in fact vary, is much simpler and does not rely on

branching universes. All that may or may not be important to determine that

measure. It just depends on the fact that the initial misalignment of the axion

angle with the QCD angle at the time of the Peccei-Quinn transition carries

very little freight in the early Universe, so it is truly random over the multiverse.

If inflation intervenes, the measure is absolutely fixed, and there is no question

that it does not interfere with any other microphysics. That is a beautiful

example when there is no alternative to anthropic reasoning.

T. Banks A question for Steinhardt. In this model, if there is some oscillation

of the scalar around its minimum as you approach the crunch, then there is

an anti-friction force on this scalar field because the universe is contracting. I

would have imagined that if you just run the equations down to the singularity

you would find that it wants to jump all over the place around the potential,

because the potential becomes irrelevant compared to the anti-friction which is

blowing up because ala goes to zero. So, if you could comment on that.

P. Steinhardt The problem you talk about would be a problem if this was a scalar

field living in an ordinary bouncing universe like the ideas that people had in

the 20s and 30s, because it would have just this problem during the contracting

phase: any kinetic energy would be blue-shifted. If you imagine, though, that

this field lives on the other brane, in the cyclic model the brane never goes