Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order

TL;DR

This paper classifies all cubic degenerate scalar-tensor Lagrangians that avoid Ostrogradsky instabilities, expanding the landscape of viable higher-order scalar-tensor theories beyond Horndeski.

Contribution

It provides a complete classification of cubic degenerate scalar-tensor Lagrangians and explores their relations to known theories via conformal and disformal transformations.

Findings

Identified all cubic degenerate Lagrangians avoiding Ostrogradsky instabilities.

Determined viable combinations with quadratic degenerate Lagrangians.

Analyzed connections to Horndeski and beyond Horndeski theories.

Abstract

We present all scalar-tensor Lagrangians that are cubic in second derivatives of a scalar field, and that are degenerate, hence avoiding Ostrogradsky instabilities. Thanks to the existence of constraints, they propagate no more than three degrees of freedom, despite having higher order equations of motion. We also determine the viable combinations of previously identified quadratic degenerate Lagrangians and the newly established cubic ones. Finally, we study whether the new theories are connected to known scalar-tensor theories such as Horndeski and beyond Horndeski, through conformal or disformal transformations.