Exact solution of an ekpyrotic fluid and a primordial magnetic field in an anisotropic cosmological space-time of Petrov D

Abstract

This document obtained and analyzed an exact solution of an ekpyrotic fluid (P = 5/3 µ) and a primordial magnetic field, so that the latter does not induce currents or electric fields. It is determined that the main role, in relation to the anisotropy in the solution, is played by the magnetic field. The solution is analyzed in points where, in appearance, some extent of singularity could exist, using the Kretschmann invariant and analyzing the metric’s functions, and it is established that this is singular at t = 0. The value of the Kretschmann invariant, in these proximities, tends to be the same as the one obtained in the case of a free ekpyrotic fluid of the magnetic field; therefore, the magnetic field is left at the background when t → 0. It is determined that the solution presents this behavior in small time values, and tends to be isotropic and equivalent to the solution of the ekpyrotic fluid obtained for the flat model of Friedmann, Robertson, Walker and Lemaitre (FRWL); for big time values, it tends to behave as the Kasner LRS solution.