Ultralight vector dark matter, anisotropies, and cosmological adiabatic modes

In this work we study the background evolution and the early time behavior of scalar cosmological perturbations with an ultralight vector dark matter. We present a model for vector dark matter in an anisotropic Bianchi type I universe. Vector fields source anisotropies in the early Universe characterized by a shear tensor which rapidly decays once the fields start oscillating, making them viable dark matter candidates. We present the set of equations needed to evolve scalar cosmological perturbations in the linear regime, both in synchronous gauge and Newtonian gauge. We show that the shear tensor has to be taken into account in the calculation of adiabatic initial conditions.