Generalized disformal Horndeski theories: Cosmological perturbations and consistent matter coupling

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.

Automated summary

By generalizing the invertible disformal transformation on Horndeski theories with higher derivatives, we have constructed a new class of ghost-free scalar-tensor theories, which we refer to as generalized disformal Horndeski theories. These theories go beyond the quadratic/cubic DHOST class. We have explored cosmological perturbations and identified a subclass where gravitational waves propagate at the speed of light and clarified the conditions for the absence of ghost/gradient instabilities for tensor and scalar perturbations. We have also investigated the conditions under which a matter field can be consistently coupled to these theories without introducing unwanted extra degrees of freedom.