General and unified solution for perfect fluid homogeneous and isotropie cosmological models

Abstract

The general and unified solution for spatially homogeneous and isotropic cosmologies containing a perfect fluid [equation of statep=(γ−1)ρ] is determined in terms of hypergeometric functions. A set of four infinitely denumerable sequences of solutions consistent with the energy conditions are shown to exist in terms of elementary functions. A generation mechanism yields the construction of all the solutions in each sequence. Using the conformal form of the metric and putting the field equations in the form of that describing the classical motion of a particle subject to a linear force, the general solution is then determined in parametric form. Closed models are analogous to harmonic oscillators, and their lifetimes are determined as an explicit function ofγ, both for conformal and cosmological times.