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

Abstract

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 level, a finding that might possibly settle the ongoing spatial curvature debate and lends even more support to the already very successful inflationary paradigm.

Model-independent constraints on $Ω_m$ and $H(z)$ from the link between geometry and growth

“…Massive, early, passivelyevolving galaxies have been found to be very good tracers in this sense (Cimatti et al 2006;Thomas et al 2011;Moresco 2015;Moresco et al 2018Moresco et al , 2020 and have been used extensively over the past two decades to measure 𝐻 (𝑧) up to 𝑧 ≈ 2. In this work we make use the 𝐻 (𝑧) measurements from CCs summarized in Table 1 of Vagnozzi et al (2021).…”

“…The literature already hosts a number of examples of the possible uses of Gaussian processes to test certain aspects of the present cosmological paradigm in model-agnostic ways. For example, one can find tests for the model dependence of the 𝐻 0 (Gómez-Valent & Amendola 2018; Cai et al 2020;Liao et al 2020;Bonilla et al 2021) and 𝑆 8 (Benisty 2021) tensions, for the non-zero curvature of space-time (Vagnozzi et al 2021;Yang & Gong 2021), as well as tests for the density and the equation of state of dark energy (Gerardi et al 2019;Zhang & Li 2018). More closely related to the topic of this work, in Perenon et al (2021) Gaussian processes were used to study the statistical correlations between the expansion history, cosmological distances, and the linear growth rate without appealing to the physical relationships between the three functions.…”

Quasar cosmology: dark energy evolution and spatial curvature

“…Moreover, the data sets listed above do not fully fit the evolu-tion of DE ranging from early to late epochs (Benetti et al 2019;Yang et al 2021) and do not fully rule out a spatially non-flat Universe (Park & Ratra 2019;Di Valentino et al 2020;Handley 2021;Yang et al 2021). The latter possibility has raised a remarkable debate about the importance of properly combining CMB data to infer significant statistical interpretations from the analysis (Planck Collaboration et al 2018;Efstathiou & Gratton 2020) and, by extension, the importance of combining data sets that do not reveal manifest tension (Vagnozzi et al 2021;Gonzalez et al 2021). Deviations from the spatially flat ΛCDM model would imply important theoretical and observational consequences and a change in our current understanding of cosmic evolution (e.g.…”

New Tsallis holographic dark energy with apparent horizon as IR-cutoff in non-flat Universe

“…Due to the involvement of positive/negative spatial curvature, certain considerations support the hypothesis of non-flat geometry. This problem can be investigated by determining the Universe spatial curvature, which is a quantity that describes the deviation of the Universe's history geometry from flat space geometry [47]. The curvature parameter Ω k , currently quantifies the useful addition mode of spatial curvature to the Universe energy density.…”