Inflation with Gauss-Bonnet Correction and Higgs Potential

TL;DR

This paper explores inflationary cosmology with a Higgs potential and Gauss-Bonnet correction, deriving equations and numerical results that align with recent observational data.

Contribution

It introduces a model combining Higgs potential and Gauss-Bonnet term, analyzing inflationary observables through numerical methods and specific functional forms.

Findings

Tensor-to-scalar ratio and spectral index match observational data.

Numerical analysis confirms the model's viability within certain parameter ranges.

Without Gauss-Bonnet, results resemble chaotic inflation predictions.

Abstract

We investigate the cosmological inflation for the Einstein-Hilbert action plus the Higgs potential function and the Gauss-Bonnet term coupled with the Higgs scalar field through a dilaton-like coupling. Then, using the Friedmann-Lema{\i}tre-Robertson-Walker metric and considering the appropriate slow-roll parameters, we derive the necessary equations of motion. In the proposed model, since the e-folding integral cannot be easily solved analytically, we first utilize a well-known Taylor expansion. Then, with a certain range of values derived for the model parameters, utilizing several plots and numerical analysis methods, we obtain results for the tensor-to-scalar ratio and the scalar spectral index that are in good agreement with the latest observational data, particularly from ACT DR6, within the acceptable range of the e-folding values. Meanwhile, a key aspect of this work, crucial for achieving reliable values of the inflationary observables, lies in the adopted functional forms for the potential and coupling functions. Also, in the absence of the Gauss-Bonnet term, we find that the inflationary observables are roughly the same as the predictions of the chaotic inflation model.