The stress-energy tensor for trans-Planckian cosmology

TL;DR

This paper derives the stress-energy tensor for a scalar field with non-linear dispersion in curved spacetime, analyzing its implications for trans-Planckian modes in cosmology and their backreaction effects during inflation.

Contribution

It provides a general derivation of the stress-energy tensor for trans-Planckian modes with non-linear dispersion relations in curved spacetime, and discusses their cosmological implications.

Findings

Trans-Planckian gravitational waves cannot explain current cosmic vacuum energy.

Backreaction effects are significant for certain dispersion relations during inflation.

In pure de Sitter inflation, the power spectrum remains unchanged except for amplitude magnification.

Abstract

This article presents the derivation of the stress-energy tensor of a free scalar field with a general non-linear dispersion relation in curved spacetime. This dispersion relation is used as a phenomelogical description of the short distance structure of spacetime following the conventional approach of trans-Planckian modes in black hole physics and in cosmology. This stress-energy tensor is then used to discuss both the equation of state of trans-Planckian modes in cosmology and the magnitude of their backreaction during inflation. It is shown that gravitational waves of trans-Planckian momenta but subhorizon frequencies cannot account for the form of cosmic vacuum energy density observed at present, contrary to a recent claim. The backreaction effects during inflation are confirmed to be important and generic for those dispersion relations that are liable to induce changes in the power spectrum of metric fluctuations. Finally, it is shown that in pure de Sitter inflation there is no modification of the power spectrum except for a possible magnification of its overall amplitude independently of the dispersion relation.