How does the curvature of the universe evolve in cyclic models?

[zeebo17]

How has the curvature of the universe changed with time?

I know that the universe is observed to nearly flat at the present time and that inflation was proposed (one of the reasons) to drive the universe to be almost perfectly flat. Do we have any idea what \Omega_k could have been like before inflation and how it changed during inflation?

Thanks!

 

[Chalnoth]

How has the curvature of the universe changed with time?

I know that the universe is observed to nearly flat at the present time and that inflation was proposed (one of the reasons) to drive the universe to be almost perfectly flat. Do we have any idea what \Omega_k could have been like before inflation and how it changed during inflation?

Thanks!

Basically, the curvature portion \Omega_k changes with the energy density as 1/a^2. So if, for instance, you are matter dominated, as matter dilutes as 1/a^3, as the universe expands curvature becomes more and more important. By contrast, during inflation, our universe was dominated by some stuff that acted much like a cosmological constant, which means its energy density was nearly independent of the expansion. So as the expansion progressed during inflation, the curvature diluted away as 1/a^2. As a result, we can't really know what it was before inflation began, as inflation set it to be nearly identically zero due to the massive increase in a during that time.

 

[Chronos]

That remains mostly in the realm of the unknowable. Our best effort to probe beyond the surface of last scattering is WMAP. The evidence is still tenuous. If we assume the universe arose from a 'big bang', we are forced to assume something prevented it from either immediately collapsing, or expanding out of view.
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[Naty1]

In a one time big bang model, as noted, so far we know little if anything before inflation, as things were apparently infinite or at least our models break down there.

But in cyclic models of the universe, where the bang is finite and mathematically consistent, such information is available. One such model is the subject of a recent book: THE ENDLESS UNIVERSE, BY Paul Steinhardt and Neil Turok, 2007. I don't recall them specifically mentioning omega in the book.