SU($N$)-natural inflation

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.

8 pages, 6 figures

References in corpus (3)

• Primordial Gravitational Waves from Axion-Gauge Fields Dynamics
• Higgsed Chromo-Natural Inflation
• The isotropic attractor solution of axion-SU(2) inflation: Universal isotropization in Bianchi type-I geometry

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• Effective Field Theory of Chiral Gravitational Waves
• How does SU($N$)-natural inflation isotropize the universe?
• Dark Energy with a Triplet of Classical U(1) Fields
• Thermal effects on warm chromoinflation