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Abstract 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 $$\xi _1$$ ξ 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 $$\xi _1$$ ξ 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.