Why is zero spatial curvature special?

TL;DR

This paper provides a theoretical motivation for why the Universe's spatial curvature is zero, using renormalization group techniques to show that flatness is a scale-free, non-singular background.

Contribution

It introduces a novel application of renormalization group methods in curved spacetime to explain the special status of zero spatial curvature in cosmology.

Findings

Zero spatial curvature is the unique scale-free, non-singular background.

Renormalization group analysis singles out flatness as a special cosmological condition.

Supports observational evidence for a flat universe with a theoretical foundation.

Abstract

Evidence for almost spatial flatness of the Universe has been provided from several observational probes, including the Cosmic Microwave Background (CMB) and Baryon Acoustic Oscillations (BAO) from galaxy clustering data. However, other than inflation, and in this case only in the limit of infinite time, there is no strong a priori motivation for a spatially flat Universe. Using the renormalization group (RG) technique in curved spacetime, we present in this work a theoretical motivation for spatial flatness. Starting from a general spacetime, the first step of the RG, coarse-graining, gives a Friedmann-Lema\^itre-Robertson-Walker (FLRW) metric with a set of parameters. Then, we study the rescaling properties of the curvature parameter, and find that zero spatial curvature of the FLRW metric is singled out as the unique scale-free, non-singular background for cosmological perturbations.