  We discuss the continuum limit of the initial data for a vacuum, closed
cosmological model with black holes as the only sources of the gravitational
field. The model we consider is an exact solution of the constraint equations
and represents a vacuum universe with a number of black holes placed on a
spatial slice of $S^3$ topology considered at the moment of its largest
expansion when the black holes are momentary at rest. We explain how and under
what conditions the FLRW metric arises as the continuum limit when the number
of black holes contained in the model goes to infinity. We also dicuss the
relation between the effective cosmological parameters of the model, inferred
from the large scale geometry of the spacetime, and the masses of individual
black holes. In particular, we prove an estimate for the difference between the
total effective mass of the system and the sum of the masses of all black
holes, thus quantifying the effects of the inhomogeneities in the matter
distribution or the cosmological backreaction.
