  The type IIB matrix model is a conjectured nonperturbative formulation of
superstring theory. Recent studies on the Lorentzian version of the model have
shown that only three out of nine spatial directions start to expand after some
critical time. On the other hand, due to the unbounded action of the Lorentzian
model, one has to introduce infrared (IR) cutoffs in order to make the
partition function finite. In this work we investigate whether the effects of
the IR cutoffs disappear in the infinite volume limit. For that purpose, we
study a simplified model with large matrix size up to $N=256$ by Monte Carlo
simulation. First we confirm the exponentially expanding behavior of the
"universe". Then we generalize the form of the IR cutoffs by one parameter, and
find that the results become universal in some region of the parameter. It is
suggested that the effects of IR cutoffs disappear in this region, which is
confirmed also from the studies of Schwinger-Dyson equations.
