Slow-roll approximations for Gauss-Bonnet inflation revisited

TL;DR

This paper revisits slow-roll approximations in Gauss-Bonnet inflation, analyzing the impact of different coupling functions on the accuracy of these approximations and providing explanations for observed behaviors.

Contribution

It compares the effectiveness of slow-roll approximations with growing coupling functions to previous decaying functions, revealing cases where more complex methods underperform.

Findings

Slow-roll approximations do not improve accuracy with growing coupling functions.

More involved approximations can sometimes be less precise than standard ones.

Explanations are provided for the varying effectiveness of different approximations.

Abstract

In our paper we consider the validity of slow-roll approximations for Gauss-Bonnet inflation introduced in [1]. In contrast to the cited paper where the coupling function before the Gauss-Bonnet term have been chosen as a decaying function of the scalar field, here we consider growing coupling functions. We have found that while in [1] new slow-roll approximations work considerably better, now they do not increase the precision. Moreover, we identify some cases where more involved approximations work worse than the standard one. Corresponding explanations of such a situation are given.