Long-wavelength metric backreactions in slow-roll inflation

TL;DR

This paper investigates second order corrections in cosmological perturbation theory during slow-roll inflation, finding that superhorizon second order effects can dominate over first order effects and resemble a cosmological constant.

Contribution

It provides a detailed analysis of second order metric backreactions in inflation, showing their potential dominance and effective cosmological constant behavior in super-Hubble regimes.

Findings

Second order corrections can dominate over first order effects in super-Hubble evolution.

Second order contributions resemble a cosmological constant in the chosen gauge.

The importance of second order effects is robust across different reasonable coordinate conditions.

Abstract

We examine the importance of second order corrections to linearized cosmological perturbation theory in an inflationary background, taken to be a spatially flat FRW spacetime. The full second order problem is solved in the sense that we evaluate the effect of the superhorizon second order corrections on the inhomogeneous and homogeneous modes of the linearized flucuations. These second order corrections enter in the form of a {\it cumulative} contribution from {\it all} of their Fourier modes. In order to quantify their physical significance we study their effective equation of state by looking at the perturbed energy density and isotropic pressure to second order. We define the energy density (isotropic pressure) in terms of the (averaged) eigenvalues associated with timelike (spacelike) eigenvectors of a total stress energy for the metric and matter fluctuations. Our work suggests that that for many parameters of slow-roll inflation, the second order contributions to these energy density and pressures may dominate over the first order effects for the case of super-Hubble evolution. These results hold in our choice of first and second order coordinate conditions however we also argue that other `reasonable` coordinate conditions do not alter the relative importance of the second order terms. We find that these second order contributions approximately take the form of a cosmological constant in this coordinate gauge, as found by others using effective methods.