Cosmic No-hair Conjecture and Inflation with an SU(3) Gauge Field

TL;DR

This paper investigates the dynamics of an SU(3) gauge field during inflation, revealing that nonlinear self-couplings generally lead to decay of anisotropies, thus supporting the cosmic no-hair conjecture, with special cases where anisotropies persist.

Contribution

It demonstrates the evolution of SU(3) gauge fields during inflation and identifies conditions under which anisotropies can survive, highlighting differences from SU(2) gauge fields.

Findings

SU(3) gauge fields tend to decay due to nonlinear self-couplings

Transient anisotropies can occur even from isotropic initial conditions

Certain gauge field components can survive due to flat directions in the potential

Abstract

We study inflationary universes with an SU(3) gauge field coupled to an inflaton through a gauge kinetic function. Although the SU(3) gauge field grows at the initial stage of inflation due to the interaction with the inflaton, nonlinear self-couplings in the kinetic term of the gauge field become significant and cause nontrivial dynamics after sufficient growth. We investigate the evolution of the SU(3) gauge field numerically and reveal attractor solutions in the Bianchi type I spacetime. In general cases where all the components of the SU(3) gauge field have the same magnitude initially, they all tend to decay eventually because of the nonlinear self-couplings. Therefore, the cosmic no-hair conjecture generically holds in a mathematical sense. Practically, however, the anisotropy can be generated transiently in the early universe, even for an isotropic initial condition. Moreover, we find particular cases for which several components of the SU(3) gauge field survive against the nonlinear self-couplings. It occurs due to flat directions in the potential of a gauge field for Lie groups whose rank is higher than one. Thus, an SU(2) gauge field has a specialty among general non-Abelian gauge fields.