The renormalization of the energy-momentum tensor for an effective initial state

TL;DR

This paper discusses how to renormalize the energy-momentum tensor for an effective initial quantum state in an expanding universe, addressing new divergences and their cancellation, and analyzing the back-reaction effects.

Contribution

It introduces a method to renormalize divergences in the energy-momentum tensor for effective initial states in inflationary backgrounds, including geometric counterterms at the initial surface.

Findings

Divergences occur only at the initial time and can be canceled by geometric counterterms.

Back-reaction from short-distance state features is small compared to vacuum energy.

The renormalization method applies to a free scalar field in an isotropic inflationary universe.

Abstract

An effective description of an initial state is a method for representing the signatures of new physics in the short-distance structure of a quantum state. The expectation value of the energy-momentum tensor for a field in such a state contains new divergences that arise when summing over this new structure. These divergences occur only at the initial time at which the state is defined and therefore can be cancelled by including a set of purely geometric counterterms that also are confined to this initial surface. We describe this gravitational renormalization of the divergences in the energy-momentum tensor for a free scalar field in an isotropically expanding inflationary background. We also show that the back-reaction from these new short-distance features of the state is small when compared with the leading vacuum energy contained in the field.