Slow-roll approximations in Einstein--Gauss--Bonnet gravity formulated in terms of e-folding numbers

TL;DR

This paper extends the slow-roll approximation in Einstein--Gauss--Bonnet gravity using e-folding numbers, assesses its accuracy, and compares reconstructed models with exact solutions and standard methods.

Contribution

It introduces a first-order slow-roll parameter based on e-folding numbers in EGB gravity and evaluates its effectiveness in model reconstruction.

Findings

Extended slow-roll approximation improves accuracy over standard methods.

Reconstructed models closely match exact solutions.

The approach enhances understanding of attractor behavior in EGB gravity.

Abstract

In the Einstein--Gauss--Bonnet (EGB) gravity models, the slow-roll approximation has been extended by taking into account the first-order slow-roll parameter $\delta_1 =-2\,H^2\,\xi^\prime/U_0$, which is proportional to the first derivative of the Gauss-Bonnet coupling function $\xi$ with respect to the e-folding number. These extensions lead to the question of the accuracy of effective potential reconstruction during the generalization of attractors in EGB gravity. We have reconstructed models using the extended slow-roll approximations and compared them with the exact expressions and the standard slow-roll approximation.