Chaotic universe, Friedmann in the mean. II. Solution of equations

Cosmological solutions are obtained to the equations for the correlators (derived from the Einstein equations in Paper I) that describe a statistically chaotic universe, Friedmann in the mean, in which delta-correlated fluctuations of amplitude h << 1 are excited. If matter has the equation of state p = nepsilon, the form of the solution will depend on where the metric perturbation spectrum reaches a maximum, that is, whether lambda/sub max/ > ct or lambda/sub max/ < ct. In a universe in which long-wavelength irrotational and vortical motions and gravitational waves (modes diverging as t → 0) are excited, the expansion will asymptotically approach the Friedmann expansion as t → infinity, and it will depend critically on n: for n < 0.26 the solution for the scale factor will lie above the Friedmann solution, while if n > 0.26 it will lie below. The influence of long-wave fluctuation modes that remain finite as t → 0 will give rise to an averaged quasi-isotropic solution. The contribution of quantum fluctuations and of the short-wave portion of the classical fluctuation spectrum to the expansion law is considered. The influence of these fluctuations will be equivalent to the contribution from an auxiliary ultrarelativistic gas having the corresponding energy density and pressure. The cosmological solutions obtained in this paper apply to a chaotic universe filled with matter that has an equation of state p-bar = nepsilon-bar (the problem is formulated and discussed in Paper I, in the preceding issue, where statistical equations are given for a chaotic universe Friedmann in the mean). In the concluding Paper III, in the next issue, constraints compatible with the observed helium abundance are placed on the degree of disorder (on the characteristics of the spectrum) which a wholly chaotic universe could have retained as it expanded to the era of nucleosynthesis