The Energy-Momentum Tensor for Cosmological Perturbations

TL;DR

This paper develops a gauge-invariant formalism for the effective energy-momentum tensor of cosmological perturbations, analyzing back-reaction effects during inflation and finding negative energy densities for long wavelength modes.

Contribution

It introduces a gauge-invariant approach to compute the energy-momentum tensor for cosmological perturbations, including scalar and tensor modes, and applies it to inflationary back-reaction.

Findings

Long wavelength scalar and tensor perturbations have negative effective energy density.

Scalar perturbations during inflation exhibit a de Sitter-like equation of state.

Back-reaction effects can counteract a cosmological constant.

Abstract

We study the effective energy-momentum tensor (EMT) for cosmological perturbations and formulate the gravitational back-reaction problem in a gauge invariant manner. We analyze the explicit expressions for the EMT in the cases of scalar metric fluctuations and of gravitational waves and derive the resulting equations of state. The formalism is applied to investigate the back-reaction effects in chaotic inflation. We find that for long wavelength scalar and tensor perturbations, the effective energy density is negative and thus counteracts any pre-existing cosmological constant. For scalar perturbations during an epoch of inflation, the equation of state is de Sitter-like.