Scalar-vector-tensor gravity theories

We construct the consistent ghost-free covariant scalar-vector-tensor gravity theories with second order equations of motion with derivative interactions. We impose locality, unitarity, Lorentz invariance and pseudo-Riemannian geometry as the fundamental terms. In the tensor sector we require diffeomorphism invariance, whereas we allow the vector sector to be gauge invariant or not. The resulting Lagrangians consist of new genuine couplings among these fields with at most two derivatives per field. They propagate five physical degrees of freedom in the gauge invariant case and six degrees of freedom if the gauge invariance is broken. In the corresponding limit of the free general functions in the Lagrangian, one recovers the generalized Proca theories. These scalar-vector-tensor theories will have important implications for cosmological and astrophysical applications, among which we mention the application to inflation and generation of primordial magnetic fields, new black hole and neutron star solutions, dark matter and dark energy.