Beyond generalized Proca theories
  We consider higher-order derivative interactions beyond second-order
generalized Proca theories that propagate only the three desired polarizations
of a massive vector field besides the two tensor polarizations from gravity.
These new interactions follow the similar construction criteria to those
arising in the extension of scalar-tensor Horndeski theories to
Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories. On the isotropic cosmological
background, we show the existence of a constraint with a vanishing Hamiltonian
that removes the would-be Ostrogradski ghost. We study the behavior of linear
perturbations on top of the isotropic cosmological background in the presence
of a matter perfect fluid and find the same number of propagating degrees of
freedom as in generalized Proca theories (two tensor polarizations, two
transverse vector modes, and two scalar modes). Moreover, we obtain the
conditions for the avoidance of ghosts and Laplacian instabilities of tensor,
vector, and scalar perturbations. We observe key differences in the scalar
sound speed, which is mixed with the matter sound speed outside the domain of
generalized Proca theories.
