  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.
