Dynamical Analysis of Anisotropic Inflation

TL;DR

This paper performs a comprehensive dynamical analysis of anisotropic inflation models involving vector fields coupled to the inflaton, confirming stability of key equilibrium points under general initial conditions.

Contribution

It provides the first thorough stability analysis of attractor solutions in anisotropic inflation with general Bianchi I initial conditions.

Findings

Confirmed stability of attractor points in previously unexamined phase-space directions

Extended stability analysis to most general Bianchi I initial conditions

Validated the robustness of anisotropic inflation models with vector coupling

Abstract

Inflaton coupling to a vector field via the $f^2(\phi)F_{\mu\nu}F^{\mu\nu}$ 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.