Observational constraints on the averaged universe

Averaging in general relativity is a complicated operation, due to the general covariance of the theory and the nonlinearity 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 Hubble Space Telescope (HST), CMB, type Ia supernovae (SNIa), and baryon acoustic oscillation (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.