SU($N$)-natural inflation

TL;DR

This paper develops a method to construct and analyze homogeneous, isotropic gauge field solutions during inflation for SU(N) gauge theories, revealing various symmetry-breaking patterns and confirming their stability through numerical simulations.

Contribution

It introduces a general procedure for finding stable, isotropic gauge field solutions during inflation for SU(N), including explicit solutions for N=3 and 4, and confirms their attractor nature.

Findings

Constructed stable solutions for SU(3) and SU(4) gauge fields during inflation.

Demonstrated the solutions are attractors via numerical analysis.

Applicable to other simple Lie groups.

Abstract

We study SU($N$) gauge fields that couple to the inflaton through the Chern-Simons term. We provide a general procedure to construct homogeneous, isotropic, and attractor solutions of the gauge fields during inflation. The gauge fields develop various VEVs corresponding to different spontaneous symmetry breaking patterns of SU($N$) where embedded SU($2$) subgroups are broken with the spatial rotation SO($3$) symmetry. As specific examples, we construct the stable solutions for $N = 3$ and $4$. We also numerically solve the gauge field dynamics and confirm that our analytic solutions are complete and attractor. It is straightforward to apply our procedure to the other simple Lie groups.