Using Spatial Curvature with H

Cheng Zong Ruan, Fulvio Melia, Yu Chen, Tong Jie Zhang

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


We present a model-independent measurement of spatial curvature Ωk in the Friedmann-Lemaitre-Robertson-Walker universe, based on observations of the Hubble parameter H(z) using cosmic chronometers, and a Gaussian process (GP) reconstruction of the H ii galaxy Hubble diagram. We show that the imposition of spatial flatness (i.e., Ωk = 0) easily distinguishes between the Hubble constant measured with Planck and that based on the local distance ladder. We find an optimized curvature parameter ωk = -0.120-0.147 +0.168 when using the former (i.e., H0 = 67.66 ± 0.42 km s-1 Mpc-1), and ωk = -0.298-0.088 +0.122 for the latter (H0 = 73.24 ± 1.74 Km s-1 Mpc-1). The quoted uncertainties are extracted by Monte Carlo sampling, taking into consideration the covariances between the function and its derivative reconstructed by GP. These data therefore reveal that the condition of spatial flatness favors the Planck measurement, while ruling out the locally inferred Hubble constant as a true measure of the large-scale cosmic expansion rate at a confidence level of ∼3σ.

Original languageEnglish (US)
Article number137
JournalAstrophysical Journal
Issue number2
StatePublished - Aug 20 2019


  • cosmological parameters
  • distance scale

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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