  Kinematical and dynamical properties of a generic inhomogeneous cosmological
model, spatially averaged with respect to free-falling (generalized
fundamental) observers, are investigated for the matter model irrotational
dust. Paraphrasing a previous Newtonian investigation, we present a
relativistic generalization of a backreaction model based on volume-averaging
the Relativistic Zeldovich Approximation. In this model we investigate the
effect of kinematical backreaction on the evolution of cosmological parameters
as they are defined in an averaged inhomogeneous cosmology, and we show that
the backreaction model interpolates between orthogonal symmetry properties by
covering subcases of the plane-symmetric solution, the Lemaitre-Tolman-Bondi
solution and the Szekeres solution. We so obtain a powerful model that lays the
foundations for quantitatively addressing curvature inhomogeneities as they
would be interpreted as Dark Energy or Dark Matter in a quasi-Newtonian
cosmology. The present model, having a limited architecture due to an assumed
FLRW background, is nevertheless capable of replacing 1/4 of the needed amount
for Dark Energy on domains of 200 Mpc in diameter for typical (one-sigma)
fluctuations in a CDM initial power spectrum. However, the model is far from
explaining Dark Energy on larger scales (spatially), where a 6% effect on 400
Mpc domains is identified that can be traced back to an on average negative
intrinsic curvature today. One drawback of the quantitative results presented
is the fact that the epoch when backreaction is effective on large scales and
leads to volume acceleration lies in the future. We discuss this issue in
relation to the initial spectrum, the Dark Matter problem, the coincidence
problem, and the fact that large-scale Dark Energy is an effect on the past
light cone (not spatial), and we pinpoint key elements of future research.
