Integration ofD-dimensional cosmological models with two factor spaces by reduction to the generalized Emden-Fowler equation

The D-dimensional cosmological model on the manifold M=R×M₁×...×M_n, describing the evolution of Einstein factor spaces M_i in the presence of a multicomponent perfect fluid source, is considered. The barotropic equation of state for the mass-energy densities and pressures of the components is assumed in each space. Where the number of non-Ricci-flat factor spaces and the number of perfect fluid components are both equal to two, the Einstein equations for the model are reduced to the generalized Emden-Fowler (second-order ordinary differential) equation, which has been recently investigated by Zaitsev and Polyanin using discrete-group analysis. We generate new integrable cosmological models using the integrable classes of this equation and present the corresponding metrics. The method is demonstrated for the special model with Ricci-flat spaces M₁ and M₂ and a two-component perfect fluid source. Translated from Teoreticheskaya i Matematicheskaya Fizika. Vol. 114, No. 3, pp. 454–469, March, 1998.