Simple Types of Anisotropic Inflation

TL;DR

This paper explores simple anisotropic inflationary solutions in gravity theories with quadratic Ricci terms, analyzing their evolution, deviations from isotropy, and potential observable effects in the cosmic microwave background.

Contribution

It introduces new anisotropic inflation models with quadratic Ricci terms and studies their evolution and observational signatures.

Findings

Anisotropic inflation solutions with constant, unequal expansion rates.

Deviations from statistical isotropy in cosmic fluctuations.

Potential for observable anisotropic effects in the microwave background.

Abstract

We display some simple cosmological solutions of gravity theories with quadratic Ricci curvature terms added to the Einstein-Hilbert lagrangian which exhibit anisotropic inflation. The Hubble expansion rates are constant and unequal in three orthogonal directions. We describe the evolution of the simplest of these homogeneous and anisotropic cosmological models from its natural initial state and evaluate the deviations they will create from statistical isotropy in the fluctuations produced during a period of anisotropic inflation. The anisotropic inflation is not a late-time attractor in these models but the rate of approach to a final isotropic de Sitter state is slow and is conducive to the creation of observable anisotropic statistical effects in the microwave background. The statistical anisotropy would not be scale invariant and the level of statistical anisotropy will grow with scale.