Constraints on the Reheating Parameters after Gauss-Bonnet Inflation from the Primordial Gravitational Waves

TL;DR

This paper investigates how the Gauss-Bonnet term influences the energy spectrum of inflationary gravitational waves and constrains reheating parameters, highlighting its role during both inflation and reheating phases.

Contribution

It provides a classification of inflation models based on tensor spectrum tilt and analyzes the impact of the Gauss-Bonnet term on gravitational wave spectra and reheating parameters.

Findings

Blue-tilted spectra are enhanced by the Gauss-Bonnet term.

Red-tilted spectra are suppressed by the Gauss-Bonnet term.

Reheating parameters are constrained by gravitational wave spectra.

Abstract

We study the effects of the Gauss-Bonnet term on the energy spectrum of inflationary gravitational waves. The models of inflation are classified into two types based on their predictions for the tensor power spectrum: red-tilted ($n_T<0$) and blue-tilted spectra ($n_T>0$), respectively, and then the energy spectra of the gravitational waves are calculated for each type of model. We find that the gravitational wave spectra are enhanced depending on the model parameter if the predicted inflationary tensor spectra have a blue tilt, whereas they are suppressed for the spectra that have a red tilt. Moreover, we perform the analyses on the reheating parameters involving the temperature, the equation-of-state parameter, and the number of $e$-folds using the gravitational wave spectrum. Our results imply that the Gauss-Bonnet term plays an important role not only during inflation but also during reheating whether the process is instantaneous or lasts for a certain number of $e$-folds until it thermalizes and eventually completes.