Dynamical Analysis of Anisotropic Inflation

Abstract

Inflaton coupling to a vector field via the $f^2(\varphi )F_{\mu \nu }{F}^{\mu \nu }$ term is used in several contexts in the literature, such as to generate primordial magnetic fields, to produce statistically anisotropic curvature perturbation, to support anisotropic inflation and to circumvent the $\eta$-problem. Here, I perform dynamical analysis of such a system allowing for most general Bianchi I initial conditions. I also confirm the stability of attractor equilibrium points in phase-space directions that had not been investigated before.

Comments: 17 pages, 2 figures