Back Reaction Problem in the Inflationary Universe

TL;DR

This paper studies how cosmological perturbations influence the inflationary universe's evolution using a renormalization-group approach, revealing effects akin to spatial curvature and radiation depending on fluctuation types.

Contribution

It introduces a gauge-invariant renormalization-group method to analyze back reaction effects of perturbations on inflationary backgrounds.

Findings

Long wavelength classical perturbations act as positive spatial curvature.

Short wavelength classical perturbations behave like radiation fluid.

Quantum fluctuations' back reaction mimics negative spatial curvature.

Abstract

We investigate the back reaction of cosmological perturbations on an inflationary universe using the renormalization-group method. The second-order zero mode solution which appears by the nonlinearity of the Einstein equation is regarded as a secular term of a perturbative expansion, we renormalized a constant of integration contained in the background solution and absorbed the secular term to this constant in a gauge-invariant manner. The resultant renormalization-group equation describes the back reaction effect of inhomogeneity on the background universe. For scalar type classical perturbation, by solving the renormalization-group equation, we find that the back reaction of the long wavelength fluctuation works as a positive spatial curvature, and the short wavelength fluctuation works as a radiation fluid. For the long wavelength quantum fluctuation, the effect of back reaction is equivalent to a negative spatial curvature.