Time-dependent supergravity solutions in null dilaton background

A class of time dependent pp-waves with NS-NS flux in type IIA string theory is considered. The background preserves 1/4 supersymmetry and may provide a toy model of Big Bang cosmology with nontrivial flux. At the Big Bang singularity in early past, the string theory is strongly coupled and matrix string model can be used to describe the dynamics. We also construct some time dependent supergravity solutions for D-branes and analyze their supersymmetry properties.