Renormalization of the quantum stress-energy tensor in inhomogeneous spacetimes: Adiabatic regularization method.

Abstract

The adiabatic regularization method, known to be a particularly efficient method for numerical study of quantum field dynamics in curved spacetimes, is applicable to evaluate the renormalized stress-energy tensor for matter in any background metric which has sufficient symmetry to allow a decomposition of the quantized field into modes. In this paper we extend this method to more general spacetimes with a small inhomogeneity which is invariant under spatial reflection. We over-come the difficulty of the mode-mixing behavior arising from the inhomogeneity of spacetime and show a possible way of obtaining the WKB solution of the time-dependent mode function under the early-time approximation. As an illustration, we investigate the renormalization of the quantum stress-energy tensor for a massive scalar field with an arbitrary curvature coupling to the inhomogeneous conformally flat spacetime. Our expressions are useful in formulating the semiclassical theory of gravity and in the numerical study of the back reaction of quantized fields in the early Universe with a small inhomogeneity.