Exploring gravitational theories beyond Horndeski

TL;DR

This paper introduces a new class of scalar-tensor gravitational theories, G^3, that extend Horndeski theories while remaining free of instabilities, and explores their properties, matter coupling, and transformations under disformal redefinitions.

Contribution

The paper defines G^3 theories, confirms their degrees of freedom, and studies their invariance under disformal transformations, extending the landscape of stable scalar-tensor theories.

Findings

G^3 theories are free of Ostrogradski instabilities.

They contain only three propagating degrees of freedom.

Disformal transformations can map G^3 subfamilies into Horndeski theories.

Abstract

We have recently proposed a new class of gravitational scalar-tensor theories free from Ostrogradski instabilities, in arXiv:1404.6495. As they generalize Horndeski theories, or "generalized" galileons, we call them G$^3$. These theories possess a simple formulation when the time hypersurfaces are chosen to coincide with the uniform scalar field hypersurfaces. We confirm that they contain only three propagating degrees of freedom by presenting the details of the Hamiltonian formulation. We examine the coupling between these theories and matter. Moreover, we investigate how they transform under a disformal redefinition of the metric. Remarkably, these theories are preserved by disformal transformations that depend on the scalar field gradient, which also allow to map subfamilies of G$^3$ into Horndeski theories.