Inflation requires initial symmetry?

[bcrowell]

I'm reading Roger Penrose's Cycles of Time. On p. 124 he's explaining why he thinks inflation doesn't solve the mystery of why the universe started out in a low-entropy state. He argues that a high-entropy collapsing FLRW universe would consist of "a horrendous mess of congealing black holes," in which the gravitational degrees of freedom would be fully activated, rather than suppressed. Then he says let's imagine time-reversing this so that we have a high-entropy big bang, which is statistically the most probable kind of big bang. Since the laws of physics governing inflation are time-reversal symmetric, the two solutions are equally valid.

In the collapsing, high-entropy universe, "...the situation will be so far from FLRW homogeneity and isotropy that the inflationary capabilities of the inflaton field will find no role, and (time-reversed) inflation will simply not take place, since this depends crucially on having an FLRW background (at least with regard to calculations that have actually been carried through)." From this he concludes that inflation has no effect on the final result of the collapse, which is a "highly complicated enormously high-entropy singularity, very possibly of a BKL type..."

Am I understanding correctly that inflation requires an isotropic and homogeneous background to start with? It gets a little confusing because he's talking about time-reversals. Forgetting about all the time-reversal stuff, and just talking about our own universe proceeding forward in time after the big bang, I think what he's saying is that it had to start out isotropic and homogeneous, because otherwise the mechanism of inflation can't get started. Is this right, and if so, is there any easy way to understand why? If this is correct, then I think he's saying that you need some degree of initial isotropy and homogeneity to allow inflation to start, and then inflation provides even more smoothing...?

 

[bapowell]

Yes, that's essentially correct. One requires a sufficiently smooth background and an energy density dominated by a homogeneous scalar field in order to get inflation started. This follows from the Friedmann Eqs. However, the rub is that the size of this initial smooth patch is found to be necessarily larger than the Hubble radius, i.e. an initial condition for inflation is that homogeneity already exists on superhorizon scales (see http://arxiv.org/abs/gr-qc/9811037" ).

Then there's always eternal inflation, which evades this whole issue because presumably the universe is either spatially infinite or truly eternal. Then, simply by chance alone you get the right conditions for inflation somewhere at some time. Once you get inflation going, it never stops.

 

[bcrowell]

Interesting -- thanks very much!