Inhomogeneous Cosmological Models and Symmetry

Abstract

Inhomogeneous cosmological models are studied extensively in the literature, in particular when the shear vanishes. The integrability properties of the field equation L _xx = F(x)L² of a spherically symmetric shear-free fluid are reviewed. A first integral, subject to an integrability condition on F(x), is found which generates a class of solutions which contains the solutions of Stephani (1983) and Srivastava (1987) as special cases. The integrability condition on F(x) is reduced to a quadrature. The Lie procedure for this equation is considered and we list various forms of F(x) and their Lie symmetry generators. A con- formal Killing vector in the t-r plane is assumed to exist and for this particular case the solution to the field equation is expressible in terms of Weierstrass elliptic functions.

It is a pleasure to dedicate this work to Jayant Narlikar on his sixteeth birthday; Jay ant’s substantial contributions to to cosmology have left a lasting impact on the subject.