Anisotropic cosmological solutions in massive vector theories

Understand

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 $1/3$.