Singularity-free Bianchi spaces with nonlinear electrodynamics

In this paper we present an analysis to determine the existence of singularities in spatially homogeneous anisotropic universes filled with nonlinear electromagnetic radiation. These spaces are conformal to Bianchi spaces admitting a three parameter group of motions 63. For these models we study geodesic completeness. It is shown that with nonlinear electromagnetic field some of the Bianchi spaces are geodesically complete (63 VIII). The analysis of the Raychaudhuri equation reveals that the BI field is responsible for the absence of singularity. When certain topology is assumed, Bianchi G ₃IX may present geodesics that are imprisoned. In the linear limit (Maxwell field) the spacetimes are singular and they do not admit a cosmological interpretation in all the range of the time coordinate.