On the curvature of the present-day Universe

TL;DR

This paper investigates whether the present-day Universe's average scalar curvature is close to zero or significantly negative, analyzing inhomogeneities and their impact on cosmological models, with implications for Dark Energy explanations.

Contribution

It provides a new formula for the averaged scalar curvature based on measurable regional quantities and assesses the validity of standard assumptions in cosmology.

Findings

Standard model requires fine-tuning of curvature assumptions.

Negative averaged curvature is favored over zero or positive.

The formula enables quantitative evaluation of curvature from inhomogeneous data.

Abstract

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.