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

Understand

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.