Reviving non-Minimal Horndeski-like Theories after GW170817: Kinetic Coupling Corrected Einstein-Gauss-Bonnet Inflation

TL;DR

This paper revisits non-minimal kinetic coupling Horndeski-like theories within Einstein-Gauss-Bonnet gravity, demonstrating how they can produce primordial gravitational waves with speed equal to light, thus aligning with GW170817 constraints, and explores their inflationary phenomenology.

Contribution

It shows how to revive certain Horndeski-like theories with kinetic couplings in Einstein-Gauss-Bonnet gravity to produce viable gravitational wave speeds post-GW170817.

Findings

Theories with kinetic coupling can produce gravitational waves with speed c_T^2=1.

Conditions on the scalar coupling function ensure massless gravitons.

The framework is viable during inflation with slow-roll and constant-roll dynamics.

Abstract

After the recent GW170817 event of the two neutron stars merging, many string corrected cosmological theories confronted the non-viability peril. This was due to the fact that most of these theories produce massive gravitons primordially. Among these theories were the ones containing a non-minimal kinetic coupling correction term in the Lagrangian, which belong to a subclass of Horndeski theories. In this work we demonstrate how these theories may be revived and we show how these theories can produce primordial gravitational waves with speed $c_T^2=1$ in natural units, thus complying with the GW170817 event. As we show, if the gravitational action of an Einstein-Gauss-Bonnet theory also contains a kinetic coupling of the form $\sim \xi(\phi) G^{\mu\nu}\partial_\mu\phi\partial_\nu\phi$, the condition of having primordial massless gravitons, or equivalently primordial gravitational waves with speed $c_T^2=1$ in natural units, results to certain conditions on the scalar field dependent coupling function of the Gauss-Bonnet term, which is also the non-minimal coupling of the kinetic coupling. We extensively study the phenomenological implications of such a theory focusing on the inflationary era, by only assuming slow-roll dynamics for the scalar field. Accordingly, we briefly study the case that the scalar field evolves in a constant-roll way. By using some illustrative examples, we demonstrate that the viability of the theoretical framework at hand may easily be achieved. Also, theories containing terms of the form $\sim \xi(\phi)\Box\phi g^{\mu\nu}\partial_\mu\phi\partial_\nu\phi$ and $\sim \xi(\phi)\left(g^{\mu\nu}\partial_\mu\phi\partial_\nu\phi\right)^2$ also lead to the same gravitational wave speed as the theory we shall study in this paper, so this covers a larger class of Horndeski theories.