Gauss-Bonnet inflation with a constant rate of roll

TL;DR

This paper explores constant-roll inflation within a Gauss-Bonnet gravity framework, deriving analytical spectra and constraining parameters using Planck 2018 data, with potential reconstruction for specific spectral cases.

Contribution

It introduces a constant Gauss-Bonnet flow parameter in constant-roll inflation, providing analytical expressions for spectra and constraining models with observational data.

Findings

Analytical scalar and tensor spectra derived using Bessel function approximation.

Parameter space constrained by Planck 2018 observations.

Scalar potential reconstructed for specific spectral cases.

Abstract

We consider the constant-roll condition in the model of the inflaton nonminimal coupling to the Gauss-Bonnet term. By assuming the first Gauss-Bonnet flow parameter $\delta_1$ is a constant, we discuss the constant-roll inflation with constant $\epsilon_1$, constant $\epsilon_2$ and constant $\eta_H$, respectively. Using the Bessel function approximation, we get the analytical expressions for the scalar and tensor power spectrum and derive the scalar spectral index $n_{\mathcal{R}}$ and the tensor to scalar ratio $r$ to the first order of $\epsilon_1$. By using the Planck 2018 observations constraint on $n_{\mathcal{R}}$ and $r$, we obtain some feasible parameter space and show the result on the $n_{\mathcal{R}}-r$ region. The scalar potential is also reconstructed in some spectral cases.