Interacting Field Theories in Robertson-Walker Spacetimes: Analytic Approximations

Abstract

The renormalization of a scalar field theory with a quartic self-coupling via adiabatic regularization in a Robertson-Walker spacetime is discussed. The adiabatic counterterms are presented in a way that is most conducive to numerical computations. A variation of the adiabatic regularization method is presented which leads to analytic approximations for the energy–momentum tensor of the quantum field and the quantum contribution to the effective mass of the mean field. Conservation of the energy–momentum tensor for the field is discussed and it is shown that the part of the energy–momentum tensor which depends only on the mean field is not conserved but the full renormalized energy–momentum tensor is conserved, as expected and required by the semiclassical Einstein's equation. It is also shown that if the analytic approximations are used the resulting approximate energy–momentum tensor is conserved. This allows a self-consistent backreaction calculation to be performed using the analytic approximations. The usefulness of the approximations is discussed.