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Is there a concordance value for $H_0$?

Vladimir V. Luković, Rocco D'Agostino, Nicola Vittorio

Abstract

We test the theoretical predictions of several cosmological models against different observables to compare the indirect estimates of the current expansion rate of the Universe determined from model fitting with the direct measurements based on Cepheids data published recently. We perform a statistical analysis of type Ia supernova (SN Ia), Hubble parameter, and baryon acoustic oscillation data. A joint analysis of these datasets allows us to better constrain cosmological parameters, but also to break the degeneracy that appears in the distance modulus definition between $H_0$ and the absolute B-band magnitude of SN Ia, $M_0$. From the theoretical side, we considered spatially flat and curvature-free $Λ$CDM, $w$CDM, and inhomogeneous Lemaître-Tolman-Bondi (LTB) models. To analyse SN Ia we took into account the distributions of SN Ia intrinsic parameters. For the $Λ$CDM model we find that $Ω_m=0.35\pm0.02$, $H_0=(67.8\pm1.0)\,$km$\,$s$^{-1}/$Mpc, while the corrected SN absolute magnitude has a normal distribution ${\cal N}(19.13,0.11)$. The $w$CDM model provides the same value for $Ω_m$, while $H_0=(66.5\pm1.8)\,$km$\,$s$^{-1}/$Mpc and $w=-0.93\pm0.07$. When an inhomogeneous LTB model is considered, the combined fit provides $H_0=(64.2\pm1.9)\,$km$\,$s$^{-1}/$Mpc. Both the Akaike information criterion and the Bayes factor analysis cannot clearly distinguish between $Λ$CDM and $w$CDM cosmologies, while they clearly disfavour the LTB model. For the $Λ$CDM, our joint analysis of the SN Ia, the Hubble parameter, and the baryon acoustic oscillation datasets provides $H_0$ values that are consistent with CMB-only Planck measurements, but they differ by $2.5σ$ from the value based on Cepheids data.

Is there a concordance value for $H_0$?

Abstract

We test the theoretical predictions of several cosmological models against different observables to compare the indirect estimates of the current expansion rate of the Universe determined from model fitting with the direct measurements based on Cepheids data published recently. We perform a statistical analysis of type Ia supernova (SN Ia), Hubble parameter, and baryon acoustic oscillation data. A joint analysis of these datasets allows us to better constrain cosmological parameters, but also to break the degeneracy that appears in the distance modulus definition between and the absolute B-band magnitude of SN Ia, . From the theoretical side, we considered spatially flat and curvature-free CDM, CDM, and inhomogeneous Lemaître-Tolman-Bondi (LTB) models. To analyse SN Ia we took into account the distributions of SN Ia intrinsic parameters. For the CDM model we find that , kmsMpc, while the corrected SN absolute magnitude has a normal distribution . The CDM model provides the same value for , while kmsMpc and . When an inhomogeneous LTB model is considered, the combined fit provides kmsMpc. Both the Akaike information criterion and the Bayes factor analysis cannot clearly distinguish between CDM and CDM cosmologies, while they clearly disfavour the LTB model. For the CDM, our joint analysis of the SN Ia, the Hubble parameter, and the baryon acoustic oscillation datasets provides values that are consistent with CMB-only Planck measurements, but they differ by from the value based on Cepheids data.

Paper Structure

This paper contains 17 sections, 27 equations, 6 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Theoretical models
  3. Friedmann-Lemaître-Robertson-Walker models
  4. LTB models
  5. Data analysis: methods
  6. SN Ia
  7. OHD
  8. BAO
  9. Combined analysis
  10. Data analysis: results
  11. Constraints on flat $\Lambda$CDM model
  12. Constraints on $k\Lambda$CDM model
  13. Constraints on $w$CDM model
  14. Constraints on LTB model
  15. SN Ia intrinsic parameters
  16. ...and 2 more sections

Figures (6)

  • Figure 1: Results at the $1\sigma$ and $2\sigma$ c.l. for the parameters of the $\Lambda$CDM model when fitted to JLA (green), OHD (azure), BAO (orange), and the three datasets combined (dark blue). Constraints from the direct measurement by Riess16 (dark red), the reanalysis by Efstathiou14 (dashed dark red), and the Planck15 (red) are also shown.
  • Figure 2: $1\sigma$, $2\sigma$ and $3\sigma$ confidence regions resulting from the fit of $k\Lambda$CDM model to the single datasets as indicated in the top right panel. The dashed line in the $\Omega_m-\Omega_\Lambda$ plane represents the transition from the decelerating (below) to the accelerating (above) models.
  • Figure 3: $1\sigma$, $2\sigma$ and $3\sigma$ confidence regions from the fits of the $w$CDM model to the single datasets as indicated in the top right panel.
  • Figure 4: $1\sigma$, $2\sigma$ and $3\sigma$ confidence regions for the LTB model to the single datasets as indicated in the top right panel.
  • Figure 5: Results at the $1\sigma$ and $2\sigma$ c.l. for $H_0$, in standard units of km s$^{-1}/{\rm Mpc}$ from our combined analysis for LTB, $w$CDM, $k\Lambda$CDM, and $\Lambda$CDM models. The results from CMB-only measurements by the Planck15 and WMAP9 and the direct estimates by Riess16 and Efstathiou14 are also shown for comparison.
  • ...and 1 more figures