Exploring gravitational theories beyond Horndeski

TLDR

G3 theories generalize Horndeski (generalized Galileons) and admit a simple formulation when time hypersurfaces align with uniform scalar field hypersurfaces. The study examines the coupling between G3 theories and matter. It also investigates how these theories transform under disformal redefinitions of the metric. The authors propose a new class of Ostrogradski‑stable scalar‑tensor theories, confirm they propagate only three degrees of freedom, and show they are preserved under gradient‑dependent disformal transformations that map subfamilies into Horndeski theories. See reference [1].

Abstract

We have recently proposed a new class of gravitational scalar-tensor theories free from Ostrogradski instabilities, in ref. [1]. 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.