No-hair conjectures, primordial shear, and protoinflationary initial conditions

Abstract

Anisotropic inflationary background geometries are analyzed in the context of an extended gauge action where the electric and magnetic susceptibilities are not bound to coincide and depend on the inflaton field. After deriving various classes of solutions with electric and magnetic hairs, we discuss the problem of the initial boundary conditions of the shear parameter and consider a globally neutral plasma as a possible relic of a preinflationary stage of expansion. While electric hairs are washed out by the finite value of the protoinflationary conductivity, magnetic hairs can persist and introduce a tiny amount of shear causing a different inflationary rate of expansion along orthogonal spatial directions. The plasma interactions are a necessary criterion to discriminate between physical and unphysical initial conditions but they are not strictly sufficient to warrant the stability of a given magnetic solution.