Late time behaviors of the expanding universe in the IIB matrix model

Recently we have studied the Lorentzian version of the IIB matrix model as a nonperturbative formulation of superstring theory. By Monte Carlo simulation, we have shown that the notion of time ---as well as space---emerges dynamically from this model, and that we can uniquely extract the real-time dynamics, which turned out to be rather surprising: after some "critical time", the SO(9) rotational symmetry of the nine-dimensional space is spontaneously broken down to SO(3) and the three-dimensional space starts to expand rapidly. In this paper, we study the same model based on the classical equations of motion, which are expected to be valid at later times. After providing a general prescription to solve the equations, we examine a class of solutions, which correspond to manifestly commutative space. In particular, we find a solution with an expanding behavior that naturally solves the cosmological constant problem.