CosmoCoffee

This seems like an interesting paper just asking for discussion! I have two comments

* Presumably there could easily be a physical prior (e.g. from string theory) that changes the conclusion about it boding "well for detecting an inflationary gravitational wave signature". For example if the underlying theory gives a prior distribution for the energy scale of inflation sharply peaked at TeV scales, then the quest may be hopeless. The actual physical prior over functions (as opposed to the Gaussian process assumed) could presumably change the conclusions about [tex]n_s[/tex] and Q.

* I'm a bit worried about using observations to determine the correct measure and ordering - e.g. using the "coolness problem" to rule out t-ordering. Surely the correct statement is if t-ordering is correct, inflation is highly disfavoured compared to almost any other model. Otherwise however wrong inflation is you can probably always keep changing your ordering/measure until you find one which gives acceptable predictions - inflation becomes even more untestable! I would think that only if you assume inflation is right can you use observation to determine the ordering: using observations to argue about the correct logic for calculation seems odd to me. (However I completely agree that t-ordering is almost certainly wrong.)

I would be interested to know how well people think the Gaussian process prior over functions encapsulates the predictions of the string landscape.

It's a long paper, I must admit I didn't quite manage to read it all!

• Where is this omega_lambda constraint coming from, phyiscally? I always thought that the fact that omega_lambda is so small is one of the biggest problems in cosmolgoy, and yet in the Figure 1 he finds that log w_lambda is between -125 and -110, in natural units, I presume, so it sort of solves this long-standing problem simply by assuming a gaussian process?
• Gaussian random process: Firstly it is not clear to me, why should this be 1-dimensional (i.e. why not d-dimensional in any random direction), or phrasing it differently: why should it be exactly white noise. Also, surely in the fourier expansion of the potential landscape, setting n=10e100 would give different results as the power in high f would just blow up (?!)
• Similar as before: not sure that putting some sort of prior on distribution of V(phi) is qualitativelly any better than putting say a gaussian prior on slow roll parameters and V(phi_0). In other words, this paper just calcualtes the implied prior on derived parameters from assuming a prior on some basic parameter. Interesting enough, but not sure whether it tells us something about physics, *unless one assumes that inflation works in a statistical-mechanical manner*, which is not at all stressed in the abstract.
• Conditioning on reference objects: one need to be careful here as reference objects are a-posteriori, i.e. you are putting in data in some form. In extreme case, if you condition on universes with omega_m=0.3 omega_lambda=0.7, etc. you are going to recover exactly this parameters. Of course, conditioning on halos or galaxy formation is much less strong but still all it gives you are the implied priors.
• This ordering ambiguity: surely this again depends on what is your basic theory, that selects how universes are picked. Unless, you know this basic theory, I don't see how this could be resolved observationally, based on one point only (our universe). (But we played this game before: if I draw a screw with a serial number 5 from a box of screws, what is the pdf for the number of screws in the box?)