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The type IIB matrix model is a promising candidate for a nonperturbativeformulation of superstring theory. In the Lorentzian version, in particular,the emergence of (3+1)D expanding space-time was observed by Monte Carlostudies of this model. Here we provide new perspectives on the (3+1)D expandingspace-time that have arised from recent studies. First it was found that thematrix configurations generated by the simulation are singular in that thesubmatrices representing the expanding 3D space have only two large eigenvaluesassociated with the Pauli matrices. This problem was conjectured to occur dueto the approximation used to avoid the sign problem in simulating the model. Inorder to confirm this conjecture, the complex Langevin method was applied toovercome the sign problem instead of using the approximation. The resultsindeed showed a clear departure from the Pauli-matrix structure, while the(3+1)D expanding behavior remained unaltered. It was also found that classicalsolutions obtained within a certain ansatz show quite generically a (3+1)Dexpanding behavior with smooth space-time structure.

New perspectives on the emergence of (3+1)D expanding space-time in the Lorentzian type IIB matrix model