Bottom-Up Reconstruction of Viable GW170817 Compatible Einstein-Gauss-Bonnet Theories

TL;DR

This paper introduces a bottom-up method to reconstruct Einstein-Gauss-Bonnet inflationary models compatible with GW170817, focusing on tensor-to-scalar ratio and predicting detectable primordial gravitational waves.

Contribution

It develops a novel bottom-up reconstruction framework for Einstein-Gauss-Bonnet theories based on tensor-to-scalar ratio, simplifying the derivation of inflationary observables.

Findings

Models predict a blue tilted tensor spectral index.

All models yield a detectable primordial gravitational wave spectrum.

Reconstruction approach simplifies connecting theory with observations.

Abstract

In this work we shall use a bottom-up approach for obtaining viable inflationary Einstein-Gauss-Bonnet models which are also compatible with the GW170817 event. Specifically, we shall use a recently developed theoretical framework in which we shall specify only the tensor-to-scalar ratio, in terms of the $e$-foldings number. Starting from the tensor-to-scalar ratio, we shall reconstruct from it the Einstein-Gauss-Bonnet theory which can yield such a tensor-to-scalar ratio, finding the scalar potential and the Gauss-Bonnet coupling scalar function as functions of the $e$-foldings number. Accordingly, the calculation of the spectral index of the primordial scalar perturbations, and of the tensor spectral index easily is greatly simplified and these observational indices can easily be found. After presenting the general formalism for the bottom-up reconstruction, we exemplify our findings by presenting several Einstein-Gauss-Bonnet models of interest which yield a viable inflationary phenomenology. These models have also an interesting common characteristic, which is a blue tilted tensor spectral index. We also investigate the predicted energy spectrum of the primordial gravitational waves for these Einstein-Gauss-Bonnet models, and as we show, all the models yield a detectable primordial wave energy power spectrum.