  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.
