RENORMALIZATION, THE TRACE ANOMALY AND SPACETIME ANISOTROPY

We investigate some aspects of the dependence of the trace anomaly on the regularization method used in the case of a scalar field with conformal coupling to gravity in a Bianchi I type universe. In the isotropic case, one of the regularization procedures one may use, the so-called 'minimal regularization', gives no trace anomaly. In the anisotropic case, however, the same procedure is no longer sufficient to remove all divergences; one must perform a further regularization, which in effect makes the whole procedure equivalent to covariant regularization; this necessarily gives a trace anomaly, which does not vanish when one takes its isotropic limit. One may thus consider that the choice of regularization procedure even in the isotropic case is forced by the more general situation, and the corresponding necessary anomaly as a remnant of the renormalized stress-energy tensor in the anisotropic case.