Revisiting cosmic no-hair theorem for inflationary settings

Abstract

In this work we revisit Wald's cosmic no-hair theorem [R. M. Wald, Phys. Rev. D 28, 2118 (1983).] in the context of accelerating Bianchi cosmologies for a generic cosmic fluid with nonvanishing anisotropic stress tensor and when the fluid energy-momentum tensor is of the form of a cosmological constant term plus a piece which does not respect strong or dominant energy conditions. Such a fluid is the one appearing in inflationary models. We show that for such a system anisotropy may grow, in contrast to the cosmic no-hair conjecture. In particular, for a generic inflationary model we show that there is an upper bound on the growth of anisotropy. For slow-roll inflationary models, our analysis can be refined further and the upper bound is found to be of the order of slow-roll parameters. We examine our general discussions and our extension of Wald's theorem for three classes of slow-roll inflationary models, generic multiscalar field driven models, anisotropic models involving U(1) gauge fields and the gauge-flation scenario.