Cosmological Backreaction for a Test Field Observer in a Chaotic Inflationary Model

TL;DR

This paper investigates how quantum fluctuations in an inhomogeneous universe affect the measured expansion rate by a test field observer during chaotic inflation, revealing a reduced effective expansion rate due to these fluctuations.

Contribution

It introduces a gauge-invariant method to compute the effective expansion rate and equation of state for a test field observer in a chaotic inflationary model, including quantum fluctuations up to second order.

Findings

Effective expansion rate is smaller than in a homogeneous universe.

Quantum fluctuations significantly influence the measured cosmological parameters.

The stochastic approach provides bounds for the validity of the approximations.

Abstract

In an inhomogeneous universe, an observer associated with a particular matter field does not necessarily measure the same cosmological evolution as an observer in a homogeneous and isotropic universe. Here we consider, in the context of a chaotic inflationary background model, a class of observers associated with a "clock field" for which we use a light test field. We compute the effective expansion rate and fluid equation of state in a gauge invariant way, taking into account the quantum fluctuations of the long wavelength modes, and working up to second order in perturbation theory and in the slow-roll approximation. We find that the effective expansion rate is smaller than what would be measured in the absence of fluctuations. Within the stochastic approach we study the bounds for which the approximations we make are consistent.