$k$-Inflation-corrected Einstein-Gauss-Bonnet Gravity with Massless Primordial Gravitons

TL;DR

This paper explores a ghost-free $k$-inflation corrected Einstein-Gauss-Bonnet model, revealing interconnected scalar functions, deriving scalar potentials, and analyzing inflationary phenomenology, including non-Gaussianities, under observational constraints.

Contribution

It introduces a ghost-free $k$-inflation Einstein-Gauss-Bonnet framework with specific scalar function relations and derives tractable scalar potentials, expanding inflationary model possibilities.

Findings

Scalar functions are interconnected under the model's constraints.

Derived scalar potentials are elegant and depend on specific assumptions.

Non-Gaussianities are significantly enhanced compared to models without $k$-inflation.

Abstract

In the present paper, we study the inflationary phenomenology of a $k$-inflation corrected Einstein-Gauss-Bonnet theory. Non-canonical kinetic terms are known for producing Jean instabilities or superluminal sound wave velocities in the aforementioned era, but we demonstrate in this work that by adding Gauss-Bonnet string corrections and assuming that the non-canonical kinetic term $\omega X^\gamma$ is in quadratic, one can obtain a ghost free description. Demanding compatibility with the recent GW170817 event forces one to accept that the relation $\ddot\xi=H\dot\xi$ for the scalar coupling function $\xi (\phi)$. As a result, the scalar functions of the theory are revealed to be interconnected and by assuming a specific form for one of them, specifies immediately the other. Here, we shall assume that the scalar potential is directly derivable from the equations of motion, once the Gauss-Bonnet coupling is appropriately chosen, but obviously the opposite is feasible as well. As a result, each term entering the equations of motion, can be written in terms of the scalar field and a relatively tractable phenomenology is produced. For quadratic kinetic terms, the resulting scalar potential is quite elegant functionally. Different exponents, which lead to either a more perplexed solution for the scalar potential, are still a possibility which was not further studied. We also discuss in brief the non-Gaussianities issue under the slow-roll and constant-roll conditions holding true, and we demonstrate that the predicted amount of non-Gaussianities is significantly enhanced in comparison to the $k$-inflation free Einstein-Gauss-Bonnet theory.