Eppur \`e piatto? The cosmic chronometer 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 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.
