  Recent studies on the Lorentzian version of the type IIB matrix model show
that (3+1)D expanding universe emerges dynamically from (9+1)D space-time
predicted by superstring theory. Here we study a bosonic matrix model obtained
by omitting the fermionic matrices. With the adopted simplification and the
usage of a large-scale parallel computer, we are able to perform Monte Carlo
calculations with matrix size up to $N=512$, which is twenty times larger than
that used previously for the studies of the original model. When the matrix
size is larger than some critical value $N_{\rm c}\simeq 110$, we find that
(3+1)D expanding universe emerges dynamically with a clear large-$N$ scaling
property. Furthermore, at sufficiently late times, we observe a power-law
behavior $t^{1/2}$ of the spatial extent with respect to time $t$, which is
reminiscent of the expanding behavior of the Friedmann-Robertson-Walker
universe in the radiation dominated era. We discuss possible implications of
this result on the original model including fermionic matrices.
