  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 non trivial 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.
