Reconstruction of the Scalar Field Potential in Inflationary Models with a Gauss-Bonnet term

TL;DR

This paper reconstructs scalar field potentials and Gauss-Bonnet coupling functions in inflationary models using observational data, analyzing implications of a blue-tilted tensor spectrum for these configurations.

Contribution

It introduces a method to reconstruct potentials and couplings in inflationary models with a Gauss-Bonnet term from observable quantities, considering the blue-tilted spectrum.

Findings

Reconstructed scalar potentials consistent with observational data.

Derived expressions for Gauss-Bonnet coupling functions.

Discussed implications of blue-tilted tensor spectrum.

Abstract

We study inflationary models with a Gauss-Bonnet term to reconstruct the scalar field potentials and the Gauss-Bonnet coupling functions from the observable quantities. Using the observationally favored relations for both $n_s$ and $r$, we derive the expressions for both the scalar field potentials and the coupling functions. The implication of the blue-tilted spectrum, $n_t>0$, of the primordial tensor fluctuations is discussed for the reconstructed configurations of the scalar field potential and the Gauss-Bonnet coupling.