We discuss simple cosmological solutions of Horava-Witten theory describing the strongly coupled heterotic string. At energies below the grand-unified scale, the effective theory is five- not four-dimensional, where the additional coordinate parameterizes a S^1/Z_2 orbifold. Furthermore, it admits no homogeneous solutions. Rather, the vacuum state, appropriate for a reduction to four-dimensional supersymmetric models, is a BPS domain wall. Relevant cosmological solutions are those associated

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... h this BPS state. In particular, such solutions must be inhomogeneous, depending on the orbifold coordinate as well as on time. We present two examples of this new type of cosmological solution, obtained by separation of variables rather that by exchange of time and radius coordinate applied to a brane solution, as in previous work. The first example represents the analog of a rolling radii solution with the radii specifying the geometry of the domain wall. This is generalized in the second example to include a nontrivial "Ramond-Ramond" scalar.