An Exact Homogeneous Stiff Cosmology that Reduces to the Kasner Solution

Abstract

A family of exact simple solutions of Einstein field equations for homogeneous stiff cosmologies is presented. The method to obtain the solution is based on the introduction of auxiliary functions in order to cast the Einstein equations in such a way that can be explicitly integrated. The obtained solution is expressed in terms of simple functions of the used coordinates. The geometrical and kinematical properties of the solution are analyzed and the parameters are restricted in order to have a physically acceptable behavior. The solution is of the Petrov type I and presents a big-bang singularity. Now, for a particular value of one of the parameters, the solution is a vacuum solution of the Bianchi I type that reduces to the Kasner solution.