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

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 ωX γ is in quadratic, one can obtain a ghost free description. Demanding compatibility with the recent GW170817 event forces one to accept that the relation ξ = H ξ for the scalar coupling function ξ(φ). 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.

Construction of inflationary scenarios with the Gauss-Bonnet term and nonminimal coupling

“…We assume that F (φ) > 0 and V (φ) > 0 during inflation. There are a lot of inflationary scenarios in Einstein-Gauss-Bonnet gravity [42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62]. The most of them includes a constant function F [44,45,46,47,49,51,53,54,55,56,57,58,59].…”