Quantum corrections to Maxwell electrodynamics in a homogeneous and isotropic universe with cosmological constant

Abstract

Some cosmological consequences of first order quantum corrections to Maxwell electrodynamics are investigated in the context of a spatially flat homogeneous and isotropic universe driven by a magnetic field plus a cosmological term $Λ$. For a vanishing $Λ$, we derive the general solution corresponding to the particular one recently found by Novello et al. [gr-qc/9806076]. We also find a general solution for the case when $Λ$ is a non-vanishing constant. Both solutions describe a non-singular, bouncing universe. However, we show that the first order correction to the electromagnetic Lagrangean density, in which the analysis is based, fails to describe the dynamics near $a_{min}$. The time range where the first order approximation can be used is explicitly evaluated. These problems my be circumvented through the use of higher order terms in the effective Lagrangean, as numerical calculations performed by Novello et al. [gr-qc/9809080], for the vanishing $Λ$ case, have indicated. A third general solution corresponding to a constant magnetic field sustained by a time dependent $Λ$ is derived. This latter solution is capable of describing the whole cosmic history and describes a universe that, although with vanishing curvature (K=0), has a scale factor that reaches a maximum and then contracts back to an arbitrarilly small size. The cosmological term decays during the initial expansion phase and increases during the late contraction phase, so as to keep $B$ constant throughout.