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