Slow-roll trajectories in Chromo-Natural and Gauge-flation Models, an exhaustive analysis

TL;DR

This paper provides a comprehensive analysis of classical solutions in the Chromo-natural inflation model, identifying parameter regions that enable successful slow-roll inflation based on initial axion field values.

Contribution

It offers an exhaustive analytical study of slow-roll trajectories in Chromo-natural and Gauge-flation models, detailing parameter constraints for inflation success.

Findings

Successful slow-roll inflation occurs within specific parameter regions.

Analytical expressions for the number of e-foldings are derived.

The behavior of solutions varies with initial axion field values.

Abstract

We present an exhaustive analysis on the classical solutions of the Chromo-natural model. We showed that starting from an arbitrary axion field value $\chi_0\in(0,f\pi)$, it is possible to have successful slow-roll inflation and working out the analytical solution of the number of e-folding, we determine the allowed region of the parameters corresponding to each $\chi_0$ value. Having the allowed parameter region, then we study the behavior of the solutions respect to the initial value of the axion field.