String Cosmology with a Time-Dependent Antisymmetric Tensor Potential

We present a class of exact solutions for homogeneous, anisotropic cosmologies in four dimensions derived from the low-energy string effective action including a homogeneous dilaton $\phi$ and antisymmetric tensor potential $B_{\mu\nu}$. Making this potential time-dependent produces an anisotropic energy-momentum tensor, and leads us to consider a Bianchi I cosmology. The solution for the axion field must then only be a linear function of one spatial coordinate. This in turn places an upper bound on the product of the two scale factors evolving perpendicular to the gradient of the axion field. The only late-time isotropic solution is then a {\em contracting} universe.