Emerging spatial curvature can resolve the conflict between
  high-redshift (CMB) and low-redshift (distance ladder) measurements of $H_0$

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Abstract

The measurements of the Hubble constant reveal a tension between high-redshift (CMB) and low-redshift (distance ladder) constraints. So far neither observational systematics nor new physics has been successfully implemented to explain this tension away. This paper present a new solution to the Hubble constant problem. It uses a relativistic simulation of the large scale structure of the Universe (the Simsilun simulation) together with the ray-tracing algorithm. The Simsilun simulation allows for relativistic and nonlinear evolution of cosmic structures, which results with a phenomenon of emerging spatial curvature, where the spatial curvature evolves from spatial flatness of the early universe towards slightly curved present-day universe. This phenomenon speeds up the expansion rate compared to the spatially flat $\Lambda$CDM model. The results of the ray-tracing analysis show that the universe which starts with initial conditions consistent with the Planck constraints should have the Hubble constant $H_0 = 72.5 \pm 2.1$ km s$^{-1}$ Mpc$^{-1}$. If the relativistic corrections are not included then the results of the simulation and ray-tracing point towards $H_0 = 68.1 \pm 2.0$ km s$^{-1}$ Mpc$^{-1}$. Thus, the inclusion of relativistic effects that lead to emergence of the spatial curvature can explain why the low-redshift measurements favour higher values compared to high-redshift constraints and alleviate the tension between the CMB and distance ladder measurements of the Hubble constant.

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Is Open Access

The Ups and Downs of the Hubble Constant

(2005)

A brief history of the determination of the Hubble constant H_0 is given. Early attempts following Lemaitre (1927) gave much too high values due to errors of the magnitude scale, Malmquist bias and calibration problems. By 1962 most authors agreed that 75< H_0 <130. After 1975 a dichotomy arose with values near 100 and others around 55. The former came from apparent-magnitude-limited samples and were affected by Malmquist bias. New distance indicators were introduced; they were sometimes claimed to yield high values of H_0, but the most recent data lead to H_0 in the 60's, yet with remaining difficulties as to the zero-point of the respective distance indicators. SNe Ia with their large range and very small luminosity dispersion (avoiding Malmquist bias) offer a unique opportunity to determine the large-scale value of H_0. Their maximum luminosity can be well calibrated from 10 SNe Ia in local parent galaxies whose Cepheids have been observed with HST. An unforeseen difficulty - affecting all Cepheid distances - is that their P-L relation varies from galaxy to galaxy, presumably in function of metallicity. A proposed solution is summarized here. The conclusion is that H_0 = 63.2 +/- 1.3 (random) +/- 5.3 (systematic) on all scales. The expansion age becomes then (with Omega_m=0.3, Omega_Lambda=0.7) 15.1 Gyr.