Two simple families of exact inhomogeneous stiff cosmologies

TL;DR

This paper presents two new families of exact inhomogeneous stiff cosmological solutions to Einstein's equations, analyzing their properties and physical acceptability, with one reducing to the Kasner vacuum solution.

Contribution

The paper introduces a novel method using auxiliary functions to derive explicit inhomogeneous stiff cosmology solutions with detailed geometrical analysis.

Findings

One solution is regular everywhere.

The second solution has a big-bang singularity.

One solution reduces to Kasner vacuum for specific parameters.

Abstract

Two families of exact simple solutions of Einstein field equations for inhomogeneous stiff cosmologies are presented. The method to obtain the solutions is based on the introduction of auxiliary functions in order to cast the Einstein equations in such a way that can be explicitly integrated. Now, despite of the equations are mathematically equivalent to the equations obtained when the source of matter is a scalar field, is worth to mention that the source that we consider is not a scalar field but a perfect fluid with the stiff equation of state. The obtained solutions are expressed in terms of simple functions of the used coordinates and two families of particular solutions are considered. The geometrical and kinematical properties of the solutions are then analyzed and the parameters are restricted in order to have a physically acceptable behavior. The two particular solutions are of the Petrov type I, the first one being regular everywhere whereas the second one presents a big-bang singularity. Now, for a particular value of one of the parameters, the second particular solution is a vacuum solution of the Bianchi I type that reduces to the Kasner solution.