Back Reaction of Cosmological Perturbations

TL;DR

This paper investigates how cosmological perturbations influence the background universe, revealing that infrared modes contribute a negative, time-growing cosmological constant, potentially explaining the small observed value of dark energy.

Contribution

It provides a diffeomorphism-invariant analysis of back-reaction effects in inflationary cosmology, highlighting the role of infrared modes in generating a dynamic relaxation of the cosmological constant.

Findings

Infrared modes dominate back-reaction in inflationary cosmology.

Back-reaction acts like a negative, time-increasing cosmological constant.

Potential mechanism for self-regulating the cosmological constant.

Abstract

The presence of cosmological perturbations affects the background metric and matter configuration in which the perturbations propagate. This effect, studied a long time ago for gravitational waves, also is operational for scalar gravitational fluctuations, inhomogeneities which are believed to be more important in inflationary cosmology. The back-reaction of fluctuations can be described by an effective energy-momentum tensor. The issue of coordinate invariance makes the analysis more complicated for scalar fluctuations than for gravitational waves. We show that the back-reaction of fluctuations can be described in a diffeomorphism-invariant way. In an inflationary cosmology, the back-reaction is dominated by infrared modes. We show that these modes give a contribution to the effective energy-momentum tensor of the form of a negative cosmological constant whose absolute value grows in time. We speculate that this may lead to a self-regulating dynamical relaxation mechanism for the cosmological constant. This scenario would naturally lead to a finite remnant cosmological constant with a magnitude corresponding to $\Omega_{\Lambda} \sim 1$.