The chaotic universe, friedmannian on the average: I

The chaotic Universe is considered, which is homogeneous and isotropic on the sealesL »L whereL is the scale of averaging. From the Einstein equations, the equations for the correlation functions have been obtained which describe the statistically chaotic model with the fluctuations of arbitrary amplitudeh. In the approximation of d-correlated fluctuations andh«1, the infinite set of coupled equations for the correlators closes and gives a self-consistent description of the inverse influence of the vortical and potential perturbations and gravitational waves with random initial phases on the Friedmann expansion of the Universe. For the state equationp=ne, the cosmological solutions have been foud.. They depend on the position of the maximum in the spectrum of the metric perturbations (?max >ct or ?max ct. The expansion of the Universe, in which the long-wave potential and vortex motions and gravitational waves are excited (the modes diverging ast ? 0), tends asymptotically to the Friedmannian one, and critically depends onn: atnn>0.26 it goes below it. The effect of the finites ast ? 0 long-wave fluctuations leads to an averaged quasi-isotropic solution. The contribution of the quantum and short-wave classical fluctuation to the expansion law is also considered. Their effect is equivalent to the contribution from an additional ultrarelativistic gas at corresponding energy density and pressure. In Paper II, the constraints on the degree of the chaos (the spectrum characteristics) of the Universe by the time of nucleosynthesis are obtained, which involve the observed helium abundance.