2021ApJ...908...84V

The question of whether cosmic microwave background (CMB) temperature and polarization data from Planck favor a spatially closed universe with curvature parameter Ω_K < 0 has been the subject of recent intense discussions. Attempts to break the geometrical degeneracy combining Planck data with external data sets such as baryon acoustic oscillation (BAO) measurements all point toward a spatially flat universe at the cost of significant tensions with Planck, which makes the resulting data set combination problematic. Settling this issue requires identifying a data set that can break the geometrical degeneracy while avoiding these tensions. We argue that cosmic chronometers (CCs), measurements of the expansion rate H(z) from the relative ages of massive early-type passively evolving galaxies, are the data set we are after. Furthermore, CCs come with the additional advantage of being virtually free of cosmological model assumptions. Combining Planck 2018 CMB temperature and polarization data with the latest CCs, we break the geometrical degeneracy and find Ω_K = -0.0054 ± 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 nonflat universe, making the resulting combination reliable. Our results allow us to assert with confidence that the universe is spatially flat to the O (10^–2) level, a finding that might possibly settle the ongoing spatial curvature debate and lends even more support to the already very successful inflationary paradigm.