A chaotic universe, Friedman in the mean. I - Statistical equations
Leonid S. Marochnik · 1980
An analysis is given of the evolution of a chaotic universe, homogeneous and isotropic only on scales L>>L-bar, where L-bar denotes the scale of averaging. The Einstein equations yield equations for the correlation functions describing a (statistically) completely chaotic model with fluctuations of arbitrary amplitude h. In the approximation of d-correlated functions and for amplitudes h<<1, the infinite interlocking system of equations for the correlators will be closed, and will provide a self-consistent description of the counter influence of spectra of vortical and irrotational perturbations and of gravitational waves with wholly random initial phases upon the expansion of a Friedmann universe. Paper II of this series will give the cosmological solutions that describe a chaotic universe Friedmann in the mean. In Paper III, constraints compatible with the observed helium abundance will be placed on the amount of disorder (i.e., on the spectrum parameters) which an initially completely chaotic universe could, in the course of its expansion, still have retained by the epoch of nucleosynthesis.