The back reaction and the effective Einstein's equation for the Universe with ideal fluid cosmological perturbations

TL;DR

This paper uses the renormalization group method to analyze how inhomogeneities in the universe influence its overall expansion, deriving an effective Einstein's equation that incorporates back reaction effects.

Contribution

It introduces a novel approach to derive an effective Einstein's equation including back reaction effects from cosmological perturbations using the renormalization group method.

Findings

Derived an effective scale factor evolution equation with back reaction effects.

Showed the effective Einstein's equation has the same form as the standard FRW equation.

Quantified the impact of inhomogeneities on cosmic expansion.

Abstract

We investigate the back reaction of cosmological perturbations on the evolution of the Universe using the renormalization group method. Starting from the second order perturbed Einstein's equation, we renormalize a scale factor of the Universe and derive the evolution equation for the effective scale factor which includes back reaction due to inhomogeneities of the Universe. The resulting equation has the same form as the standard Friedman-Robertson-Walker equation with the effective energy density and pressure which represent the back reaction effect.