Not all adiabatic vacua are physical states

TL;DR

The paper demonstrates that lower-order adiabatic vacua are physically unreasonable due to singularities in the energy-momentum tensor, and critiques a recent large momentum expansion method for regularization.

Contribution

It shows that adiabatic vacua of order less than four are not physically acceptable and analyzes the limitations of a proposed large momentum expansion scheme.

Findings

Adiabatic vacua below order four develop singularities.

Lower-order adiabatic vacua are not physically reasonable.

A recent large momentum expansion scheme fails to reproduce the trace anomaly.

Abstract

Adiabatic vacua are known to be Hadamard states. We show, however that the energy-momentum tensor of a linear Klein-Gordon field on Robertson-Walker spaces developes a generic singularity on the initial hypersurface if the adiabatic vacuum is of order less than four. Therefore, adiabatic vacua are physically reasonable only if their order is at least four. A certain non-local large momentum expansion of the mode functions has recently been suggested to yield the subtraction terms needed to remove the ultraviolet divergences in the energy-momentum tensor. We find that this scheme fails to reproduce the trace anomaly and therefore is not equivalent to adiabatic regularisation.