Ultralight vector dark matter, anisotropies and cosmological adiabatic modes

Ultralight dark matter models have recently gained interest due to its small scales predictions. Their small masses may let them behave as a collection of waves, leading to new phenomena such as a suppression in the mass power spectrum on small scales, the presence of characteristic interference patterns, the formation of soliton cores. In this talk I will consider an ultralight vector field dark matter (VFDM) model with an homogeneous background field pointing in a given direction. 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. I will present recent results on the study of the evolution of the background universe with VFDM and large-scale cosmological perturbations in the linear regime, such as the matter power spectrums defined for wave vectors with a given direction.