Macroscopic Einstein Equations for a Cosmological Model with $\lambda$-term

TL;DR

This paper derives macroscopic Einstein equations for a flat, isotropic universe filled with gravitational radiation, providing analytical solutions describing its evolution from ultrarelativistic to inflationary regimes.

Contribution

It introduces a novel averaging method for Einstein equations over gravitational perturbations, resulting in a closed system of equations for cosmological evolution.

Findings

Derived a closed system of differential equations for the universe's evolution.

Obtained an asymptotic solution for gravitational perturbation amplitude.

Analytically described the transition from ultrarelativistic to inflationary expansion.

Abstract

Through averaging the Einstein equations over transverse gravitational perturbations it is obtained a closed system of two ordinary differential equations describing macroscopic cosmological evolution of the isotropic space-flat Universe filled with gravitational radiation. It is found an asymptotic solution of evolution equation for gravitational perturbation amplitude. Making the substitution of this solution into Einstein equation averaged over gravitational perturbations, the single evolution non-linear ordinary differential second-order equation relative to macroscopic scale factor is obtained. It is also found a solution of evolution equation for scale factor in WKB-approximation which analytically describes the process of transformation from ultrarelativistic regime of cosmological extension to inflationary one.