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

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.