Renormalized Stress Tensor for trans-Planckian Cosmology

TL;DR

This paper derives finite, renormalized expressions for the stress tensor of a scalar field with generalized dispersion relations in cosmology, using adiabatic renormalization and dimensional regularization, linking to modifications in fundamental constants.

Contribution

It introduces a method to compute finite stress tensor expressions in trans-Planckian cosmology with generalized dispersion relations, connecting renormalization to redefinitions of cosmological and Newton constants.

Findings

Finite stress tensor expressions obtained via adiabatic renormalization.

Dimensional regularization used to evaluate divergent integrals.

Renormalization corresponds to redefinition of fundamental constants.

Abstract

Finite expressions for the mean value of the stress tensor corresponding to a scalar field with a generalized dispersion relation in a Friedman--Robertson--Walker universe are obtained using adiabatic renormalization. Formally divergent integrals are evaluated by means of dimensional regularization. The renormalization procedure is shown to be equivalent to a redefinition of the cosmological constant and the Newton constant in the semiclassical Einstein equations.