Observational Constraints on the Averaged Universe

TL;DR

This paper explores how the process of averaging in general relativity affects cosmological models, revealing that geometric and dynamical curvatures decouple, which complicates constraining dark energy and requires better understanding of averaging effects.

Contribution

It demonstrates the decoupling of geometrical and dynamical spatial curvature in averaged cosmological models and assesses observational constraints on this phenomenon.

Findings

Geometrical spatial curvature is tightly constrained by data.

Decoupling impacts the ability to constrain dark energy.

Understanding averaging effects is crucial for accurate cosmological modeling.

Abstract

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.