which one in particular? There was a dozen of them at this point already – COBE, WMAP (still orbiting), ACBAR, Planck was just launched etc. etc.

Cheers,
Dmitry.

Sure, if you really say that your prescription picks up adiabatic vacuum, then I agree (that’s what I was aiming to ).

Cheers and thanks for explanations, I think your paper is quite a piece of work!

Cheers,
Dmitry.

As I remember, the BD vacuum used to just mean the alpha=0 (in the Allen parameterization) choice of the dS invariant alpha vacuum before 2004/5 when the whole transplanckian business was all the rage. But these days (for better or for worse), people generally use the term BD vacuum to mean the usual positive frequency Minkowski vacuum in the limit of (k/a)>>H when these modes are created to sto speak, i.e. the one that is adiabatic and does not lead to particle production when the universe expands, even if we are not really in dS space but instead just in near-dS inflationary spacetime. The prescription we used picks up this vacuum — one can show this by using our prescription to calculate the 2-pt correlation. We use the term BD vacuum to refer to this.

I hope this answers your question! Apologies for a bit tardy!

Best,
Eugene

let me slightly reformulate the question. B.-D., Allen-Mottola and adiabatic vacua describe similar physics at subhorizon scales and differ at superhorizon scales. Since, as you say, inflation starts at some particular moment of time , you don’t want to specify the state of modes which are superhorizon at that moment of time, since you’ll never have access to them (am I correct?) If so, probably the best choice of vacuum in the initial moment of time would be adiabatic vacuum – since choosing this vacuum you only specify corr. properties of modes which are subhorizon at . On the other hand, if you want to glue a contracting patch of dS to the expanding patch, then the appropriate initial condition would be in vacuum state (one of the A.M. vacua, see Bousso, Maloney, Strominger for example).

I understood the part about prescription, but the question I wanted to ask is really the following: why do you say that this particular prescription corresponds exactly to Bunch-Davies vacuum (and not, say, some other vacuum)?

Cheers,
Dmitry.

The effect of vacuum choice is essentially the same as the choice initial conditions. Choosing the adiabatic, or Bunch-Davies vacuum amounts to selecting the initial state that has no particle content. The epsilon prescription is basically a way of preparing the initial state. Inflation didn’t really start in the infinite past, but here we merely use this as a trick to ensure that any initial transients are well damped away. Choosing a different initial state can be loosely thought of as choosing a state that initially has some particle content. Although we haven’t given this a tremendous amount of thought, it is our opinion that with different initial conditions there should be no spurious divergences in the loops – provided the calculation is done properly. Each choice of vacuum will have an analogous prescription which prevents these spurious divergences from arising.

The effect on nan-Gaussianities of choosing an excited initial state built over a Bunch-Davies vacuum was considered by Tolley and Holman (arXiv:0710.1302). Since one has particle content initially, one sees effects which are proportional to the number of e-foldings of inflation – or the time elapsed since inflation began. This is not surprising since the interactions can no longer be thought of as being adiabatically turned on, the amount of interaction will be proportional to the amount of time elapsed. As well as these initial state signatures, excited states allow different momentum configurations. One can pick up so-called “folded triangles.” 3pt correlations functions with folded triangle momenta are those with momentum amplitude k1=2k2=2k3, hence one can only construct a triangle where all three modes essentially point in either the same or directly opposite directions.

I hope this answers your question!

Best,
Peter

here is the first question of mine: suppose I select a different vacuum state – say, an Allen-Mottola vacuum that differs from B.-D. or arbitrary adiabatic vacuum for quasi-dS, to be as general as possible. To which extent will it affect the final result for NG? For example, will I generate spurious divergences choosing a different initial vacuum state?

Cheers,
Dmitry.