Eppur è piatto? The Cosmic Chronometers Take on Spatial Curvature and Cosmic Concordance

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 would require identifying a dataset which can break the geometrical degeneracy while not incurring in these tensions. In this work 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 compilation of 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. After discussing our results in light of the oldest objects in the Universe, we assess their stability against against minimal parameter space extensions and CC systematics, finding them to be stable against both. We find no substantial tension between Planck and CC data within a non-flat Universe, making the resulting combination reliable. Our results therefore allow us to assert with confidence that the Universe is indeed 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.