Dynamics of inflation with mutually orthogonal vector fields in a closed universe

TL;DR

This paper investigates the complex dynamics of a closed universe with vector fields, revealing how spatial curvature influences inflation and stability, especially in models involving SU(2) gauge fields and axion interactions.

Contribution

It introduces a new ansatz for vector fields without non-abelian symmetry and analyzes their effects on inflationary dynamics in a closed universe.

Findings

Vector fields slightly increase universe stability against collapse.

Spatial curvature causes unconventional pre-inflationary effects.

Numerical analysis of axion-SU(2) and U(1)$\times$U(1)$\times$U(1) models.

Abstract

We study the dynamics of a homogeneous, isotropic, and positively curved universe in the presence of a SU(2) gauge field or a triplet of mutually orthogonal vector fields. In the SU(2) case we use the previously known ansatz for the gauge-field configuration, but the case without non-abelian symmetries is more nontrivial and we develop a new ansatz. We in particular consider axion-SU(2) inflation and inflation with vector fields having U(1)$\times$U(1)$\times$U(1) symmetry, and analyze their dynamics in detail numerically. Novel effects of the spatial curvature come into play through vector fields, which causes unconventional pre-inflationary dynamics. It is found that the closed universe with vector fields is slightly more stable against collapse than that filled solely with an inflaton field.