Revisiting Cosmic No-Hair Theorem for Inflationary Settings

TL;DR

This paper revisits Wald's cosmic no-hair theorem in the context of inflationary cosmologies, showing that anisotropy can grow under certain conditions and establishing bounds related to slow-roll parameters.

Contribution

It extends Wald's theorem to inflationary models with anisotropic stress, providing bounds on anisotropy growth in various inflationary scenarios.

Findings

Anisotropy may grow in inflationary settings contrary to the original no-hair conjecture.

Upper bounds on anisotropy growth are related to slow-roll parameters.

The analysis applies to multiple inflationary models, including multi-scalar and gauge field scenarios.

Abstract

In this work we revisit Wald's cosmic no-hair theorem in the context of accelerating Bianchi cosmologies for a generic cosmic fluid with non-vanishing 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 multi-scalar field driven models, anisotropic models involving U(1) gauge fields and the gauge-flation scenario.