Same state as in the Big Bang in a collapsing universe?

[Suekdccia]

TL;DR Summary

Is it possible that if the universe collapses, it reaches the same state as in its beginning?

Suppose the universe were to eventually collapse in a Big Crunch [1]. How closely could the universe's final moments resemble those at the beginning of the universe? Could the universe return to its original state exactly in some kind of "Big Crunch" or "Big Bounce" model?

[1]: https://en.wikipedia.org/wiki/Big_Crunch

 

[PeterDonis]

Suppose the universe were to eventually collapse in a Big Crunch [1]. How closely could the universe's final moments resemble those at the beginning of the universe?

Not close at all. In such a universe, the Big Bang has uniform density everywhere to a very good approximation, i.e., no gravitational clumping has occurred. But over the history of the universe, gravitational clumping does occur--the matter clumps into galaxies, stars, planets, and eventually into black holes. So the Big Crunch will be highly non-uniform, very different from the Big Bang.

 

[Ken G]

This has indeed been a criticism aimed at "oscillating universe" models, there would seem to be a constant increase in entropy (in the form of greater inhomogeneity in the matter, energy, and gravity) that could not "reboot" the same Big Bang conditions. It should be noted, however, that Nobel laureate Roger Penrose feels he has an answer to that: the "conformal cyclic cosmology" (https://en.wikipedia.org/wiki/Conformal_cyclic_cosmology). It's pretty technical, but the basic idea seems to be that you don't need Big Crunches, you just need infinite expansions to achieve such low densities that there is, in some sense, nothing to anchor down the space (not his way of saying it, but it's what I'm taking from it), allowing for what he calls "conformal rescaling." I think the essence of it is that the universe periodically loses track of its own size scale, and acts like it is once again very dense and hot. The entropy problem goes away in this rescaling event, and like waves lapping at the shore, you get behavior that acts like one Big Bang after another without any Big Crunches in between. I can't speak to its plausibility, Roger Penrose knows more GR in any one of his nerve ganglions than I know in my whole brain.