Analysis of Vector-Inflation Models Using Dynamical Systems

TL;DR

This paper investigates vector-field inflation models using dynamical systems, identifying conditions for sustained inflation and analyzing critical points related to gauge-fixing terms in U(1) and SU(2) models.

Contribution

It introduces a dynamical systems approach to analyze vector-field inflation models with gauge-fixing and potential terms, identifying inflationary critical points.

Findings

Critical points correspond to inflation in both models

Conditions for at least 60 efolds of inflation are derived

Gauge-fixing terms influence the inflationary dynamics

Abstract

We analyze two possible vector-field models using the techniques of dynamical systems. The first model involves a U(1)-vector field and the second a triad of SU(2)-vector fields. Both models include a gauge-fixing term and a power-law potential. A dynamical system is formulated and it is found that one of the critical points, for each model, corresponds to inflation, the origin of these critical points being the respective gauge-fixing terms. The conditions for the existence of an inflationary era which lasts for at least 60 efolds are studied.