Bumblebee field as a source of cosmological anisotropies

In this work, a bumblebee field is adopted in order to generate cosmological anisotropies. For that purpose, we assume a Bianchi I cosmology, as the background geometry, and a bumblebee field coupled to it. Bumblebee models are examples of a mechanism for the Lorentz symmetry violation by assuming a nonzero vacuum expectation value for the bumblebee field. When coupled to the Bianchi I geometry, which is not in agreement with a cosmological principle, the bumblebee field plays the role of a source of anisotropies and produces a preferred axis. Thus, a fraction of the cosmic anisotropies would come from the Lorentz symmetry violation. In the last part of the article, we try to assume an upper bound on the bumblebee field using the quadrupole and octopole moments of the cosmic microwave background radiation.