Not all adiabatic vacua are physical states

Adiabatic vacua are known to be Hadamard states. We show, however that the energy-momentum tensor of a linear Klein-Gordon eld 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 nd that this scheme fails to reproduce the trace anomaly and therefore is not equivalent to adiabatic regularisation. e-mail: [email protected] Not all Adiabatic Vacua 1