Generalized disformal Horndeski theories: cosmological perturbations and consistent matter coupling

TL;DR

This paper introduces a new class of ghost-free scalar-tensor theories derived from generalized disformal transformations of Horndeski theories, analyzing their cosmological perturbations and matter coupling for stability and consistency.

Contribution

It constructs generalized disformal Horndeski theories beyond existing DHOST classes and examines their perturbative stability and matter coupling conditions.

Findings

Identified subclasses with gravitational waves propagating at light speed

Established conditions for absence of ghost and gradient instabilities

Determined criteria for consistent matter coupling without extra degrees of freedom

Abstract

Invertible disformal transformations are a useful tool to investigate ghost-free scalar-tensor theories. By performing a higher-derivative generalization of the invertible disformal transformation on Horndeski theories, we construct a novel class of ghost-free scalar-tensor theories, which we dub generalized disformal Horndeski theories. Specifically, these theories lie beyond the quadratic/cubic DHOST class. We explore cosmological perturbations to identify a subclass where gravitational waves propagate at the speed of light and clarify the conditions for the absence of ghost/gradient instabilities for tensor and scalar perturbations. We also investigate the conditions under which a matter field can be consistently coupled to these theories without introducing unwanted extra degrees of freedom.