  To support the validity of a factorizable metric ansatz used in string
cosmology, we investigate a toy problem in RSI model. For this purpose, we
revise the gradient expansion method to conform to the factorizable metric
ansatz. By solving the 5-dimensional equations of motion and substituting the
results into the action, we obtain the 4-dimensional effective action. It turns
out that the resultant action is equivalent to that obtained by assuming the
factorizable metric ansatz. Our analysis gives the support of the validity of
the factorizable metric ansatz.
