Integration of D-dimensional 2-factor Spaces Cosmological Models by Reducing to the Generalized Emden-fowler Equation
نویسنده
چکیده
The D-dimensional cosmological model on the manifold M = R × M1 × M2 describing the evolution of 2 Einsteinian factor spaces, M1 and M2, in the presence of multicomponent perfect fluid source is considered. The barotropic equation of state for mass-energy densities and the pressures of the components is assumed in each space. When the number of the non Ricci-flat factor spaces and the number of the perfect fluid components are both equal to 2, the Einstein equations for the model are reduced to the generalized EmdenFowler (second-order ordinary differential) equation, which has been recently investigated by Zaitsev and Polyanin within discrete-group analysis. Using the integrable classes of this equation one generates the integrable cosmological models. The corresponding metrics are presented. The method is demonstrated for the special model with Ricci-flat spaces M1,M2 and the 2-component perfect fluid source. PACS numbers: 04.20.J, 04.60.+n, 03.65.Ge
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