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Recently we have shown by Monte Carlo simulation that expanding(3+1)-dimensional universe appears dynamically from a Lorentzian matrix modelfor type IIB superstring theory in (9+1)-dimensions. The mechanism for thespontaneous breaking of rotational symmetry relies crucially on thenoncommutative nature of the space. Here we study the classical equations ofmotion as a complementary approach. In particular, we find a unique class ofSO(3) symmetric solutions, which exhibits the time-dependence compatible withthe expanding universe. The space-space noncommutativity is exactly zero,whereas the space-time noncommutativity becomes significant only towards theend of the expansion. We interpret the Monte Carlo results and the classicalsolution as describing the behavior of the model at earlier time and at latertime, respectively.

Expanding universe as a classical solution in the Lorentzian matrix model for nonperturbative superstring theory