Healthy scalar-tensor theories with third-order derivatives: Generalized disformal Horndeski and beyond

TL;DR

This paper develops a new class of ghost-free scalar-tensor theories with third-order derivatives, extending Horndeski and U-DHOST frameworks, ensuring only physical degrees of freedom propagate.

Contribution

It introduces a systematic construction of extended scalar-tensor theories with third-order derivatives that remain ghost-free and generalize existing Horndeski and U-DHOST models.

Findings

Constructed ghost-free scalar-tensor theories with third-order derivatives.

Extended the framework of generalized disformal Horndeski and U-DHOST theories.

Analyzed transformation properties under disformal transformations.

Abstract

We systematically construct ghost-free scalar-tensor theories whose Lagrangian includes up to third-order derivatives of the scalar field. Using a spatially covariant action written in terms of the ADM variables, we impose degeneracy and consistency conditions that ensure the propagation of only one scalar and two tensor degrees of freedom. The resultant theories extend the generalized disformal Horndeski and U-DHOST theories. We discuss the transformation properties of these theories under generalized disformal transformations.