On the Effects of Non-metricity in an Averaged Universe

TL;DR

This paper investigates how non-metricity, arising from averaging in macroscopic gravity, affects the geometry and observable distances in the universe, highlighting that back-reaction influences are limited to the Hubble parameter.

Contribution

It reinterprets back-reaction effects as non-metricity in averaged geometry and derives modified geometric and cosmological equations within this framework.

Findings

Non-metricity affects geodesic kinematics and geometry.

Modified Raychaudhuri and Sachs equations are derived.

Non-metricity influences angular diameter distance only via the Hubble parameter.

Abstract

In the covariant averaging scheme of macroscopic gravity, the process of averaging breaks the metricity of geometry. We reinterpret the back-reaction within macroscopic gravity in terms of the non-metricity of averaged geometry. This interpretation extends the effect of back-reaction beyond mere dynamics to kinematics of geodesic bundles. With a 1+3 decomposition of the spacetime, we analyse how geometric flows are modified by deriving the Raychaudhuri and Sachs equations. We also present the modified forms of Gauss and Codazzi equations. Finally, we derive an expression for the angular diameter distance in Friedmann Lema\^itre Robertson Walker universe and show that non-metricity modifies it only through the Hubble parameter. Thus, we caution against overestimating the influence of back-reaction on the distances.