The Back Reaction of Gravitational Perturbations and Applications in Cosmology

TL;DR

This paper develops a gauge-invariant framework to analyze the back reaction of cosmological perturbations, including gravitational waves and scalar fluctuations, on the universe's evolution, with applications to inflation and the cosmological constant problem.

Contribution

It introduces a gauge-invariant formulation of the back reaction problem for generic perturbations, extending beyond high-frequency cases, and applies it to inflationary scenarios.

Findings

Back reaction of long-wavelength fluctuations can counteract the cosmological constant.

Gauge invariance simplifies the analysis of back reaction effects.

Back reaction effects are consistent with fundamental conservation laws.

Abstract

We study the back reaction of cosmological perturbations on the evolution of the universe. The object usually employed to describe the back reaction of perturbations is called the effective energy-momentum tensor (EEMT) of cosmological perturbations. In this formulation, the problem of the gauge dependence of the EEMT must be tackled. We advance beyond traditional results that involve only high frequency perturbations in vacuo, and formulate the back reaction problem in a gauge invariant manner for completely generic perturbations. We give a quick proof that the EEMT for high-frequency perturbations is gauge invariant which greatly simplifies the pioneering approach by Isaacson. As applications we analyze the back reaction of gravitational waves and scalar metric fluctuations in Friedmann-Robertson-Walker background spacetimes. We investigate in particular back reaction effects during inflation in the Chaotic scenario. Fluctuations with a wavelength much bigger than the Hubble radius during inflation contribute a negative energy density, and in that case back reaction counteracts any pre-existing cosmological constant. Finally, we set up the equations of motion for the back reaction on the geometry and on the matter, and show how they are perfectly consistent with the Bianchi identities and the continuity equations.