  We propose a new method for studying the early universe in the Lorentzian
version of the IIB matrix model, which is considered to be a nonperturbative
formulation of superstring theory. This method is based on the idea of
renormalization group, and it enables us to study the time-evolution of the
universe for much longer time than in the previous work, which showed that the
SO(9) rotational symmetry is spontaneously broken down to SO(3) after a
"critical time". We demonstrate how this method works in a simplified model,
which is expected to capture the behaviors of the original model when the space
is not so large. In particular, we present clear evidence that the
three-dimensional space expands exponentially after the critical time in this
simplified model.
