Universality of linear perturbations in SU($N$)-natural inflation

TL;DR

This paper demonstrates that a broad class of SU(N)-based inflation models with pseudo-scalar fields exhibit universal predictions for linear perturbations, akin to chromo-natural inflation, depending on a single parameter combination.

Contribution

It proves the universality of linear perturbation predictions across SU(N)-natural inflation models, extending chromo-natural inflation results to a wider class with a single parameter dependence.

Findings

Predictions depend on the parameter gλ, unifying different models.

SU(N) models share the same n_s-r predictions as chromo-natural inflation.

Potential for transitions in λ during inflation and observational implications.

Abstract

We prove the universality of predictions for linear perturbations from the entire class of models of inflation driven by a pseudo-scalar field coupled to an SU($N$) gauge boson, where SU($2$) subgroups in the SU($N$) crossed with the background spatial SO($3$) spontaneously break into a single SO($3$). The effect of which SU($2$) subgroup in SU($N$) acquires a VEV through spontaneous symmetry breaking can be quantified by a single parameter $\lambda$, which always appears in combination with the gauge coupling constant $g$. In the linear perturbations, as well as the background system, the same dynamics and predictions as in the chromo-natural inflation hold for its SU($N$) extension by replacing $g \to g\lambda$. The latter models thereby draw the same prediction curve on the $n_s$-$r$ plane as the former at the tree level as long as $g \lambda$ stays constant during inflation. We briefly discuss possible transitions from one value of $\lambda$ to another during inflation and the observational prospects.