Reconstruction of inflation from scalar field non-minimally coupled with the Gauss-Bonnet term

TL;DR

This paper investigates early-time inflation within a scalar-tensor gravity model coupled with the Gauss-Bonnet term, deriving conditions for viability and reconstructing the model's Lagrangian based on observational data.

Contribution

It introduces a method to reconstruct the inflationary Lagrangian in a scalar-Gauss-Bonnet model consistent with Planck data, extending previous models with a novel approach.

Findings

Derived spectral index and tensor-to-scalar ratio matching observations

Reconstructed the Lagrangian for a viable inflationary scenario

Identified conditions for the model's compatibility with Planck data

Abstract

In this paper, we analyze the early-time inflation in a scalar-tensor theory of gravity where the scalar field is minimally coupled with the Gauss-Bonnet four dimensional topological invariant. The theory belongs to a class of Horndeski models where the field equations are at the second order like in General Relativity. A viable inflationary scenario must correctly reproduce the last Plank satellite data. By starting from some simple assumptions on the field and on the coupling function between the field and the Gauss-Bonnet term, we derive the spectral index and the tensor-to-scalar ratio of the model. Once the model is viable, it is finally possible to fully reconstruct its Lagrangian.