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This is a dramatic illustration of the fact that any amount of observational data, necessarily restricted to the past lightcone and necessarily with non-zero errors, cannot predict anything mathematically about the future even one hour hence without further assumptions. It is also a display of the difference between mathematics and physics: the physicist necessarily employs intuition about the real world.

I'm confused by the final statement that we can't predict anything without further assumptions. It's a function of the complexity of the model, surely. If we have a simple model so that all the relevant constants are fixed by the observations, then they uniquely predict the future. However, if your model is complicated and has parameters unconstrained by experiment, then you can choose them to give "ripping" cosmologies within the hour. This is why we like to choose models that make sense (which is our intuition, as they say, for example to not have silly things like phantom fields, and why we choose to work within rigorous frameworks and seek to embed or motivate models within them), and also why we do model comparison. It may be possible to have some rip within the hour, but we can quantify how unlikely that is given the data, or how unlikely it is within the landscape. The statement they give is very deep sounding, but I think it has very little content.

The authors construct exact instanton solutions for tunneling over very small barriers in the presence of gravity, and demonstrate matching between previous results, and with the flat potential and no gravity case. Confusingly, it seems that for consistency one should include the tunneling effect along side the rolling of a field on a flat potential, even when there is no barrier. I'm not sure quite what this means operationally, but I think it may have effects for models of quintessence where the asymptotic future is a big crunch. Here it seems we may not be able to consider simple scalar field rolling, but may also have to include the instanton effects. More excuses to go back and read Coleman-DeLuccia again are always good.

A long paper on measures in Cosmology, which I haven't read in its entireity yet. However, I found the final comment in the abstract quite provocative and interesting: "In a universe where the second law of thermodynamics holds, one cannot make use of our knowledge of the present state of the universe to "retrodict" the likelihood of past conditions." This is due to laws being time symmetric, while in practice we have the second law. In practice we *must* resort to Occam's razor and/or beauty arguments. Later: "if one wishes to make an argument in favor of inflation having occurred in the early universe, this argument must be based upon its being a simple and/or elegant hypothesis that accounts for observed phenomena. Any argument about the "likelihood" of inflation based upon the Liouville (or other) measure on phase space will require a justification for the use of this measure." Sometimes, beauty and Occam's razor are incompatible, or rather scale dependent (as in the case of the string landscape), and from a purely philosophical point of view I don't feel entriely comfortable with either being used as a criterion of truth when trying to discover things about the universe. However, this paper makes this seem inevitable. Certainly food for thought.