Multidimensional Cosmology with $m$-Component Perfect Fluid

TL;DR

This paper develops a cosmological model with multiple Einstein spaces and perfect-fluid matter components, solving Einstein and Wheeler-DeWitt equations for specific cases, including quantum wormhole solutions for a single fluid component.

Contribution

It provides exact solutions to Einstein and Wheeler-DeWitt equations in multidimensional cosmology with multi-component perfect fluids, including quantum wormhole solutions for the single-component case.

Findings

Exact solutions for Einstein equations with Ricci-flat spaces.

Integration of Wheeler-DeWitt equations in special cases.

Quantum wormhole solutions for single-component fluid.

Abstract

A cosmological model describing the evolution of $n$ Einstein spaces $(n>1)$ with $m$-component perfect-fluid matter is considered. When all spaces are Ricci-flat and for any $\alpha$-th component the pressures in all spaces are proportional to the density: $p_{i}^{(\alpha)} = (1- h_{i}^{(\alpha)}) \rho^{(\alpha)}$, $h_{i}^{(\alpha)}$ = const, the Einstein and Wheeler-DeWitt equations are integrated in the cases: i) $m=1$, for all $h_{i}^{(\alpha)}$; ii) $m > 1$, for some special sets of $h_{i}^{(\alpha)}$. For $m=1$ the quantum wormhole solutions are also obtained. \\