  The Lorentzian type IIB matrix model is a promising candidate for a
non-perturbative formulation of superstring theory. However, it was found
recently that a Euclidean space-time appears in the conventional large-$N$
limit. In this work, we add a Lorentz invariant mass term to the original model
and consider a limit, in which the coefficient of the mass term vanishes at
large $N$. By performing complex Langevin simulations to overcome the sign
problem, we observe the emergence of expanding space-time with the Lorentzian
signature.
