  A refined version of a recently introduced method for analysing the dynamics
of an inhomogeneous irrotational dust universe is presented. A fully
non-perturbative numerical computation of the time dependence of volume in this
framework leads to the following results. If the initial state of the universe
is Einstein-de Sitter with small Gaussian perturbations, then there is no
acceleration even though the inhomogeneities strongly affect the evolution. A
universe with a positive background curvature can exhibit acceleration, but not
in conjunction with reasonable values for the Hubble rate. Thus the correct
values for both quantities can be achieved only by introducing a positive
cosmological constant. Possible loopholes to this conclusion are discussed; in
particular, acceleration as an illusion created by peculiarities of light
propagation in an inhomogeneous universe is still possible. Independently of
the cosmological constant question, the present formalism should provide an
important tool for precision cosmology.
