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 ξ1, 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 ξ1 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.