Could you comment on Big Snap scenario briefly mentioned by Max Tegmark on page 12 (and I can't google more):

How unitary cosmology generalizes thermodynamics and solves the inflationary entropy problem http://arxiv.org/abs/1108.3080

I understand that during the inflation the number of degrees of freedom per hubble volume decreases, so life will be impossible. However, isn't it the same as "Big Chill" - cold empty dark universe?

Eh, I doubt the "Big Snap" will turn out to be a real issue.

My argument is this. You can fully-describe our universe by only referencing the observable universe and the horizon set by the value of the cosmological constant: the degrees of freedom on this horizon encapsulate all of the degrees of freedom outside this horizon. In this model, the number of degrees of freedom is finite, constant, and independent of the dynamics of the expanding universe, so that you don't need to have any granulation effects in order to end up with a constant degrees of freedom.

Edit: Cool. He actually discusses this alternative approach. So it generally comes down to whether or not the holographic cosmology which I just laid out above is accurate. I think it is more likely to be, but we'll see (hopefully).

But this is true only without dark energy, with it the matter (together with the associated degrees of freedom) constantly goes away thru the hubble horizon, so we can end with an absolutely empty Hubble volume, without a single particle.

No, the situation I described was with dark energy (specifically, a cosmological constant). Yes, it may look very different in terms of the number of particles. But that doesn't mean it isn't the same system. Particles that leave the horizon have their degrees of freedom encoded in the horizon.

The end future of this universe is not an absolutely empty Hubble volume, by the way, because there is Hawking radiation from the horizon.

Edit: Oh, and as for how the degrees of freedom are encoded on the horizon, I don't think anybody knows exactly (I'm sure many understand it better than I). But the horizon does grow in size with every particle that passes through it (analogous to the fact that a black hole's horizon grows with every particle that enters the black hole's horizon).

I know. Even more: Hawking radiation "blocks" the Big Rip: very close to the rip, Hubble volumes become so tiny that the Hawking radiation (it's intensity grows much faster that the deterioration of space!) fills the space again with the particles, effectively "resetting" the expansion. I don't know if anybody had ever explored that model.

And it's a pity because I that was my very next question :)