shown by Monte Carlo simulation that (3+1)-dimensional expanding space-time appears from the Lorentzian version of the model [@Kim:2011cr]. The time scale that has been probed by the simulation is typically of the order of the Planck scale. This line of research has been continued in Refs. [@Ito:2013ywa; @Ito:2015mxa; @Ito:2017rcr; @Azuma:2017dcb; @Aoki:2019tby; @Nishimura:2019qal], whereas the Euclidean version has been investigated in Refs. [@Anagnostopoulos:2013xga; @Anagnostopoulos:2017gos] and references therein.

In order to probe the space-time at later times than the Planckian time, we need to increase the matrix size by many orders of magnitude, which is not feasible in numerical simulations. On the other hand, it is expected that the classical approximation is valid at late times because the action becomes large due to the expansion of space. Various classical solutions that allow cosmological interpretations have been found [@Kim:2011ts; @Kim:2012mw; @Chaney:2015ktw; @Steinacker:2017vqw], and a systematic method for constructing classical solutions was also developed [@Kim:2012mw]. (See also Refs. [@Steinacker:2019awe; @Steinacker:2019fcb; @Manolakos:2019tdf] for related papers in this direction.) However, the class of solutions that has been constructed so far looks too simple to describe our real world.

In fact, solving the classical equation of motion in the type IIB matrix model is quite different from 