Bianchi type I cosmology with a Kalb-Ramond background field

An effect of the Lorentz symmetry breaking is pointed out in the cosmological context. Using a Bianchi I geometry coupled to the Kalb-Ramond field, a consequence of the Lorentz symmetry violation is indicated by a different rate of expansion in a given spatial direction. This article focuses on the coupling constant $\xi_1$, which generates, from the Kalb-Ramond field, all three coefficients that give rise to the Lorentz violation in the gravity sector of the minimal Standard Model Extension. The coupling constant $\xi_1$ increases the rate of expansion of the universe in a given direction during a dark energy era. As a consequence, a range of validity of that coupling constant is also obtained.