Slow-roll inflation with a Gauss-Bonnet correction

TL;DR

This paper develops an analytical framework for slow-roll inflation models with Gauss-Bonnet corrections, revealing how such terms can modify observable predictions and potentially revive previously disfavored inflation potentials.

Contribution

It introduces a hierarchy of flow functions to analytically derive power spectra in Gauss-Bonnet inflation, breaking the standard consistency relation and applying the formalism to constrain models with observational data.

Findings

Gauss-Bonnet terms can alter the tensor-to-scalar ratio.

The formalism breaks the standard consistency relation.

Certain Gauss-Bonnet couplings can revive quartic inflation models.

Abstract

We consider slow-roll inflation for a single scalar field with an arbitrary potential and an arbitrary nonminimal coupling to the Gauss-Bonnet term. By introducing a combined hierarchy of Hubble and Gauss-Bonnet flow functions, we analytically derive the power spectra of scalar and tensor perturbations. The standard consistency relation between the tensor-to-scalar ratio and the spectral index of tensor perturbations is broken. We apply this formalism to a specific model with a monomial potential and an inverse monomial Gauss-Bonnet coupling and constrain it by the 7-year Wilkinson Microwave Anisotropy Probe data. The Gauss-Bonnet term with a positive (or negative) coupling may lead to a reduction (or enhancement) of the tensor-to-scalar ratio and hence may revive the quartic potential ruled out by recent cosmological data.