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The emergence of (3+1)-dimensional expanding space-time in the Lorentziantype IIB matrix model is an intriguing phenomenon which was observed in MonteCarlo studies of this model. In particular, this may be taken as a support tothe conjecture that the model is a nonperturbative formulation of superstringtheory in (9+1) dimensions. In this paper we investigate the space-timestructure of the matrices generated by simulating this model and its simplifiedversions, and find that the expanding part of the space is describedessentially by the Pauli matrices. We argue that this is due to anapproximation used in the simulation to avoid the sign problem, which actuallyamounts to replacing $e^{iS_{\rm b}}$ by $e^{\beta S_{\rm b}}$ ($\beta>0$) inthe partition function, where $S_{\rm b}$ is the bosonic part of the action. Wealso discuss the possibility of obtaining a regular space-time with the(3+1)-dimensional expanding behavior in the original model with the correct$e^{iS_{\rm b}}$ factor.

On the structure of the emergent 3d expanding space in the Lorentzian type IIB matrix model