Cosmological perturbations with ultralight vector dark matter fields: numerical implementation in CLASS

In this work we consider a dark matter candidate described by an ultralight vector field, whose mass is in principle in the range $H_{\rm{eq}}\sim 10^{-28}\rm{eV}\ll m< \rm{eV}$. The homogeneous background vector field is assumed to point in a given direction. We present a numerical implementation of cosmological perturbations in a Bianchi type I geometry with vector field dark matter in a modified version of the Cosmic Linear Anisotropy Solving System (CLASS). We study the evolution of large-scale cosmological perturbations in the linear regime. We compute the matter power spectrums defined for Fourier modes pointing in a given direction. We obtain interesting features in the power spectrums whose observational significance depends on the field mass. We compare the results with the standard $\rm{\Lambda CDM}$ and with the corresponding well-studied ultralight scalar field dark matter case. As for the scalar case we obtain a suppression in the power spectrums at small scales characterized by the same scale, namely the Jeans scale. The main characteristic feature of the vector field model we notice here for first time is that the amplitude of the suppression effect depends on the direction of the Fourier modes with respect to the background vector field, leaving eventually a possible anisotropic imprint in structure formation at small scales.