### Alpha Vacua

In light of my previous entry, I thought a closer look at Danielsson’s paper on α-vacua was in order.

There are several objections to the proposal that the initial state of the inflaton be an α-vacuum.

**The Equivalence Principle:**At length scales much shorter than the radius of curvature of de Sitter space, physics should be Minkowskian. But the α-vacua don’t approach the Minkowski vacuum at short distances.

Danielsson’s response is that, if inflation starts not too long after the Planck time, then there*are*no length scales “much shorter than the radius of curvature of de Sitter space” at which effective field theory is valid.**Acausal Singularities of the Green’s Functions:**The Green’s functions in the α-vacuum have quite screwy behaviour outside the lightcone.

But, responds Danielsson, “physical” Green’s functions, like commutators or retarded Green’s functions*do*vanish outside the lightcone, just like in Minkowski space. Even in Minkowski space, “unphysical” Green’s functions, like the Feynman propagator are nonvanishing outside the lightcone.**Screwy Perturbation Theory:**Similarly, says Danielsson, one might have thought that pertubation theory (loop amplitudes) was sick in an α-vacuum. But it isn’t.**The Exit Problem:**The Bunch-Davies vacuum matches onto the Minkowski vacuum when we exit from inflation. Of course we don’t want to end up precisely in the Minkowski*vacuum*; we want the universe to reheat. But we don’t want a boatload of ultra-energetic particles either.

Here, I think, the response is less satisfactory. Danielsson argues that the effects may possibly evade the observational limits. But this is clearly still a big problem for the α-vacuum “scenario”.