> This looks like an eternal inflation model Yes, and the particular one I was thinking about was Carroll & Chen arXiv:hep-th/0410270. Rather than an expandin

> This looks like an eternal inflation model Yes, and the particular one I was thinking about was Carroll & Chen arXiv:hep-th/0410270. Rather than an expanding cosmology < (t-axis horizontal; x vertical) or an expanding and recollapsing <>, they have something closer to ><, which close to what I had in mind with, "... RW metric [might not be] always-expanding or always-contracting". Of course <> fits that too. I'm not sure we're really disagreeing on anything now - I think that we agree that while the homogeneity-on-every-slice constraint is a useful picture for many things, it's not really useful for distinguishing the ends of time of e.g. a collapsing universe with three crucial epochs: one that's smooth and low entropy, one that's lumpy and higher entropy, and one that's even higher entropy, exactly (as you wrote) because that's not what the standard model can yield on its own; you need to perturb around the model, for instance. Once you're doing that, you're not doing physics in the model sensu stricto. But surely for a question like this we want to depart from homogeneity on every slice? For smoothness I just assume that reheating after inflation does that and we get clumping after baryogenesis. For a recollapsing universe (with eventual galaxies), if you can give me a sketch of a mechanism for dismantling late-epoch structure into something reasonably similar to the dark ages in our universe, I'd go away and have a think about think about how to distinguish the different ends of time. But otherwise, I agree '"big crunch" state would be very different--lots and lots of inhomogeneities being magnified by the collapse' and argue that distinguishes the two ends of time sufficiently that a thermodynamic arrow of time points towards increasing entropy. > If you choose the initial configuration precisely enough Yes, that's the kernel of the argument. > > in a collapsing background, can we have observed systems in which Boltzmann entropy is increasing? > Why not? Let me try to tighten the wording: in a collapsing universe where the entropy the entropy at one end of time is higher than the entropy at the other, can we have long-lived mutually-interacting systems where one is decreasing in Boltzmann entropy as it gets closer to the higher-entropy end, while the other is increasing in Boltzmann entropy as it gets closer to the higher-entropy end? Or does the one with more DOF's "correct" the other?