Eppur \`e piatto? The cosmic chronometer take on spatial curvature and cosmic concordance

TL;DR

This paper demonstrates that cosmic chronometers combined with Planck CMB data can effectively break the degeneracy on spatial curvature, providing strong evidence for a flat Universe with minimal model assumptions.

Contribution

It introduces cosmic chronometers as a robust dataset to resolve spatial curvature debates without significant tensions or model dependencies.

Findings

Combined Planck and CC data favor a flat Universe with a7_K a7 -0.0054 a7 a7 0.0055.

Results are stable against minimal parameter extensions and systematics.

No substantial tension found between Planck and CC data in a non-flat Universe.

Abstract

The question of whether Cosmic Microwave Background (CMB) temperature and polarization data from Planck favor a spatially closed Universe with curvature parameter $\Omega_K<0$ has been the subject of recent intense discussions. Attempts to break the geometrical degeneracy combining Planck data with external datasets such as Baryon Acoustic Oscillation (BAO) measurements all point towards a spatially flat Universe, at the cost of significant tensions with Planck, which make the resulting dataset combination problematic. Settling this issue requires identifying a dataset which can break the geometrical degeneracy while not incurring in these tensions. We argue that cosmic chronometers (CC), measurements of the expansion rate $H(z)$ from the relative ages of massive early-type passively evolving galaxies, are the dataset we are after. Furthermore, CC come with the additional advantage of being virtually free of cosmological model assumptions. Combining Planck 2018 CMB temperature and polarization data with the latest CC measurements, we break the geometrical degeneracy and find $\Omega_K=-0.0054 \pm 0.0055$, consistent with a spatially flat Universe and competitive with the Planck+BAO constraint. Our results are stable against minimal parameter space extensions and CC systematics, and we find no substantial tension between Planck and CC data within a non-flat Universe, making the resulting combination reliable. Our results allow us to assert with confidence that the Universe is spatially flat to the ${\cal O}(10^{-2})$ level, a finding which might possibly settle the ongoing spatial curvature debate, and lends even more support to the already very successful inflationary paradigm.