Generalized disformal Horndeski theories: Cosmological perturbations and consistent matter coupling

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