  Fluctuation terms and higher moments of a quantum state imply corrections to
the classical equations of motion that may have implications in early-universe
cosmology, for instance in the state-dependent form of effective potentials. In
addition, space-time properties are relevant in cosmology, in particular when
combined with quantum corrections required to maintain general covariance in a
consistent way. Here, an extension of previous investigations of static
quasiclassical space-time models to dynamical ones is presented, describing the
evolution of 1-dimensional space as in the classical Lemaitre--Tolman--Bondi
models. The corresponding spatial metric has two independent components, both
of which are in general subject to quantum fluctuations. The main result is
that individual moments from both components are indeed required for general
covariance to be maintained at a semiclassical level, while quantum
correlations between the components are less relevant.
