The IIB matrix model has been suggested as a particular formulation
of nonperturbative superstring theory (M-theory).
It has now been realized that an emerging classical spacetime may
reside in its large-$N$ master field.
This bosonic master field can, in principle, give rise to Minkowski
and Robertson-Walker spacetimes.
The outstanding task is to solve the bosonic master-field equation,
which is essentially an algebraic equation.
In this article, we present new results for
the $(D,\,N)=(10,\,4)$ bosonic master-field equation of the
IIB matrix model,
where $D$ is the number of bosonic matrices and $N$ the matrix size.
We also give, in a self-contained appendix, explicit results for
critical points of the effective bosonic action.
The main physics application of the (dimensionless) IIB matrix model
may be in providing a (conformal) phase that replaces the
Friedmann big bang singularity.