Here you go Meow, this is way above my understanding although I do get the basic idea, my argument here is that Carol offers an alternate model not that it is correct or that it proves anything. Indeed Carol is quick to point out that he is not asserting that his model proves anything in the debate.
Spontaneous Inflation and the Origin of the Arrow of Time
Thanks for this. I'm just going to look at the abstract and conclusion with a peek at the meat to see how it affects the discussion:
Abstract said:We suggest that spontaneous eternal inflation can provide a natural explanation for the thermodynamic arrow of time, and discuss the underlying assumptions and consequences of this view. In the absence of inflation, we argue that systems coupled to gravity usually evolve asymptotically to the vacuum, which is the only natural state in a thermodynamic sense. In the presence of a small positive vacuum energy and an appropriate inflaton field, the de Sitter vacuum is unstable to the spontaneous onset of inflation at a higher energy scale. Starting from de Sitter, inflation can increase the total entropy of the universe without bound, creating universes similar to ours in the process. An important consequence of this picture is that inflation occurs asymptotically both forwards and backwards in time, implying a universe that is (statistically) time-symmetric on ultra-large scales.
Translation: time's arrow is given by the entropic gradient ("thermodynamic arrow of time"), without inflation, systems coupled to gravity are singular (there are singularities). With positive vacuum energy (this should be understood that the positivity comes in contrast with the potential of gravity), positive scalar manifolds with Lorentz invariance is still unstable (and given an inflaton field, it's going to blow up).
Inflation is a free lunch (as Paul Davies would say), and our universe is an expected outcome. However, there are past and future timelike geodesics that are timelike at infinity given the methodology.
Ok, so really not too far off from Vilenkin/Borde/Guth.
Let's look at the conclusion. It's couched in the Discussion section from what I can see, but this part stuck out to me:
Discussion said:By taking seriously the ability of spacetime to expand and dilute degrees of freedom, we claim to have shown how an arrow of time can naturally arise dynamically in the course of the evolution from a generic boundary condition. In the classification introduced in Section 2, our proposal imagines that there do not exist any maximum-entropy equilibrium states, but rather that the entropy can increase from any starting configuration. This is not, of course, sufficient; it is also necessary to imagine that the path to increasing the entropy naturally creates regions of spacetime resembling our observable universe. In the presence of a nonzero vacuum energy and an appropriate inflaton field, we suggest that thermal fluctuations from de Sitter space into eternal inflation provide precisely the correct mechanism.
This is unequivocally saying that the universe did not have an ontological beginning given the premises of the paper. If the "arrow of time" (the entropic gradient) can arise dynamically from generic boundary conditions, then we can have a "beginning" that is not an ontological beginning.
So, I guess the point of me asking to see this was to just verify that it's a good response to Craig's argument. Add another paper to the pile that says Craig has very little idea what he's talking about cosmologically.