Healthy scalar-tensor theories with third-order derivatives: Generalized disformal Horndeski and beyond
We systematically construct a broad class of 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 remove the additional Ostrogradsky degree of freedom and leave one scalar and two tensor degrees of freedom within the regular branch considered in this paper. The resulting class extends the generalized disformal Horndeski and U-DHOST families.
gr-qc↗