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November 7, 2002

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”.
Posted by distler at November 7, 2002 4:58 PM

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