Towards supersymmetric cosmology in M theory

We present a new solution in the heterotic M-theory in which the metric depends on (cosmic) time. The solution preserves N=1 supersymmetry in 4 dimensions in the leading order of the ${\kappa }^{2\mathrm{/}3}$ expansion. It is the first example of the time-dependent supersymmetric solution in M-theory on $S^1\mathrm{/}{Z}_2$. It describes expanding 4-dimensional space-time with shrinking orientifold interval and static Calabi-Yau internal space.