Cosmology in beyond-generalized Proca theories
  The beyond-generalized Proca theories are the extension of second-order
massive vector-tensor theories (dubbed generalized Proca theories) with two
transverse vector modes and one longitudinal scalar besides two tensor
polarizations. Even with this extension, the propagating degrees of freedom
remain unchanged on the isotropic cosmological background without an
Ostrogradski instability. We study the cosmology in beyond-generalized Proca
theories by paying particular attention to the dynamics of late-time cosmic
acceleration and resulting observational consequences. We derive conditions for
avoiding ghosts and instabilities of tensor, vector, and scalar perturbations
and discuss viable parameter spaces in concrete models allowing the dark energy
equation of state smaller than $-1$. The propagation speeds of those
perturbations are subject to modifications beyond the domain of generalized
Proca theories. There is a mixing between scalar and matter sound speeds, but
such a mixing is suppressed during most of the cosmic expansion history without
causing a new instability. On the other hand, we find that derivative
interactions arising in beyond-generalized Proca theories give rise to
important modifications to the cosmic growth history. The growth rate of matter
perturbations can be compatible with the redshift-space distortion data due to
the realization of gravitational interaction weaker than that in generalized
Proca theories. Thus, it is possible to distinguish the dark energy model in
beyond-generalized Proca theories from the counterpart in generalized Proca
theories as well as from the $\Lambda$CDM model.
