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Recent studies on the Lorentzian version of the type IIB matrix model showthat (3+1)D expanding universe emerges dynamically from (9+1)D space-timepredicted by superstring theory. Here we study a bosonic matrix model obtainedby omitting the fermionic matrices. With the adopted simplification and theusage of a large-scale parallel computer, we are able to perform Monte Carlocalculations with matrix size up to $N=512$, which is twenty times larger thanthat used previously for the studies of the original model. When the matrixsize 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-$N$ scalingproperty. Furthermore, at sufficiently late times, we observe a power-lawbehavior $t^{1/2}$ of the spatial extent with respect to time $t$, which isreminiscent of the expanding behavior of the Friedmann-Robertson-Walkeruniverse in the radiation dominated era. We discuss possible implications ofthis result on the original model including fermionic matrices.

Power-law expansion of the Universe from the bosonic Lorentzian type IIB matrix model