Cosmological implication of antisymmetric tensor field on D-brane

We discuss the cosmological implications of an antisymmetric tensor field when it experiences a kind of ``Higgs mechanism,‘’ including nonlocal interaction terms, on D-branes. Even when a huge magnetic-condensation-inducing anisotropy is assumed in the early universe, the expansion of the universe leads to an isotropic $B$-matter-dominated universe.