  We discuss the effect of curvature and matter inhomogeneities on the averaged
scalar curvature of the present-day Universe. Motivated by studies of averaged
inhomogeneous cosmologies, we contemplate on the question whether it is
sensible to assume that curvature averages out on some scale of homogeneity, as
implied by the standard concordance model of cosmology, or whether the averaged
scalar curvature can be largely negative today, as required for an explanation
of Dark Energy from inhomogeneities. We confront both conjectures with a
detailed analysis of the kinematical backreaction term and estimate its
strength for a multi-scale inhomogeneous matter and curvature distribution. Our
main result is a formula for the spatially averaged scalar curvature involving
quantities that are all measurable on regional (i.e. up to 100 Mpc) scales. We
propose strategies to quantitatively evaluate the formula, and pinpoint the
assumptions implied by the conjecture of a small or zero averaged curvature. We
reach the conclusion that the standard concordance model needs fine-tuning in
the sense of an assumed equipartition law for curvature in order to reconcile
it with the estimated properties of the averaged physical space, whereas a
negative averaged curvature is favoured, independent of the prior on the value
of the cosmological constant.
