Stability analysis of chromo-natural inflation and possible evasion of Lyth's bound

TL;DR

This paper thoroughly analyzes the stability of chromo-natural inflation, identifying conditions for stability and showing how the model can produce detectable gravitational waves while evading the traditional Lyth bound.

Contribution

It provides a complete stability analysis of chromo-natural inflation, clarifying the parameter space where the model is viable and can generate observable gravitational waves.

Findings

Stable inflation occurs for vector mass m_g > 2H.

Scalar perturbations cause instability when m_g < 2H.

Model can produce detectable gravitational waves while evading Lyth's bound.

Abstract

We perform the complete stability study of the model of chromo-natural inflation (Adshead and Wyman '12), where, due to its coupling to a SU(2) vector, a pseudo-scalar inflaton chi slowly rolls on a steep potential. As a typical example, one can consider an axion with a sub-Planckian decay constant f. The phenomenology of the model was recently studied (Dimastrogiovanni, Fasiello, and Tolley '12) in the m_g >> H limit, where m_g is the mass of the fluctuations of the vector field, and H the Hubble rate. We show that the inflationary solution is stable for m_g > 2 H, while it otherwise experiences a strong instability due to scalar perturbations in the sub-horizon regime. The tensor perturbations are instead standard, and the vector ones remain perturbatively small. Depending on the parameters, this model can give a gravity wave signal that can be detected in ongoing or forthcoming CMB experiments. This detection can occur even if, during inflation, the inflaton spans an interval of size Delta chi = O (f) which is some orders of magnitude below the Planck scale, evading a well known bound that holds for a free inflaton (Lyth '97).