A chaotic universe, Friedmann in the mean. II - Solution of equations

Cosmological solutions are obtained to the equations for the correlators that describe a statistically chaotic universe, Friedmann in the mean, in which delta-correlated fluctuations of amplitude h much less than 1 are excited. If matter has the equation of state p = n(epsilon), the form of the solution will depend on where the metric perturbation spectrum reaches a maximum. In a universe in which long-wavelength irrotational and vortical motions and gravitational waves (modes diverging as t approaches zero) are excited, the expansion will asymptotically approach the Friedmann expansion as t approaches infinity, and it will depend critically on n. The contribution of quantum fluctuations and of the short-wave portion of the classical fluctuation spectrum to the expansion law is also considered. The influence of these fluctuations will be equivalent to the contribution from an auxiliary ultrarelativistic gas having the corresponding energy density and pressure.