Observational Constraints on the Averaged Universe
  Averaging in general relativity is a complicated operation, due to the
general covariance of the theory and the non-linearity of Einstein's equations.
The latter of these ensures that smoothing spacetime over cosmological scales
does not yield the same result as solving Einstein's equations with a smooth
matter distribution, and that the smooth models we fit to observations need not
be simply related to the actual geometry of spacetime. One specific consequence
of this is a decoupling of the geometrical spatial curvature term in the metric
from the dynamical spatial curvature in the Friedmann equation. Here we
investigate the consequences of this decoupling by fitting to a combination of
HST, CMB, SNIa and BAO data sets. We find that only the geometrical spatial
curvature is tightly constrained, and that our ability to constrain dark energy
dynamics will be severely impaired until we gain a thorough understanding of
the averaging problem in cosmology.
