Cosmological solutions of Hořava-Witten theory

We discuss cosmological solutions of Hořava-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 parametrizes an $S^1{/Z}_2$ orbifold. Furthermore, it admits no homogeneous solutions. Rather, the static vacuum state, appropriate for a reduction to four-dimensional $N=1\mathrm{}$ supersymmetric models, is a BPS domain wall pair. Relevant cosmological solutions are those associated with 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 than by exchange of the time and radius coordinates of a brane solution, as in previous work. The first example represents the analogue of a rolling radii solution with the radii specifying the geometry of the domain wall pair. This is generalized in the second example to include a nontrivial “Ramond-Ramond” scalar.