Covariant point-splitting regularization for a scalar quantum field in a Robertson-Walker universe with spatial curvature

Abstract

We evaluate the vacuum stress tensor for a massless scalar quantum field in a general Robertson-Walker background spacetime, and that for a massive field in the special case of the Einstein universe, using covariant point-splitting regularization. A comparison is made with previous partial results of Ford, and Dowker & Critchley. It is shown that the stress tensor expectation value is a local, geometrical object in the massless case, and its explicit form is fixed by using the known value of the conformal anomaly. The existence of a type of vacuum entropy and temperature is demonstrated for the static models with space curvature.