Anisotropic cosmological solutions in massive vector theories
  In beyond-generalized Proca theories including the extension to theories
higher than second order, we study the role of a spatial component $v$ of a
massive vector field on the anisotropic cosmological background. We show that,
as in the case of the isotropic cosmological background, there is no additional
ghostly degrees of freedom associated with the Ostrogradski instability. In
second-order generalized Proca theories we find the existence of anisotropic
solutions on which the ratio between the anisotropic expansion rate $\Sigma$
and the isotropic expansion rate $H$ remains nearly constant in the
radiation-dominated epoch. In the regime where $\Sigma/H$ is constant, the
spatial vector component $v$ works as a dark radiation with the equation of
state close to $1/3$. During the matter era, the ratio $\Sigma/H$ decreases
with the decrease of $v$. As long as the conditions $|\Sigma| \ll H$ and $v^2
\ll \phi^2$ are satisfied around the onset of late-time cosmic acceleration,
where $\phi$ is the temporal vector component, we find that the solutions
approach the isotropic de Sitter fixed point ($\Sigma=0=v$) in accordance with
the cosmic no-hair conjecture. In the presence of $v$ and $\Sigma$ the early
evolution of the dark energy equation of state $w_{\rm DE}$ in the radiation
era is different from that in the isotropic case, but the approach to the
isotropic value $w_{\rm DE}^{{\rm (iso)}}$ typically occurs at redshifts $z$
much larger than 1. Thus, apart from the existence of dark radiation, the
anisotropic cosmological dynamics at low redshifts is similar to that in
isotropic generalized Proca theories. In beyond-generalized Proca theories the
only consistent solution to avoid the divergence of a determinant of the
dynamical system corresponds to $v=0$, so $\Sigma$ always decreases in time.
