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Hubble parameter measurement constraints on the redshift of the deceleration-acceleration transition, dynamical dark energy, and space curvature

Omer Farooq, Foram Madiyar, Sara Crandall, Bharat Ratra

TL;DR

This work updates the $H(z)$ data compilation to 38 measurements spanning $0.07\le z\le 2.36$ and uses them to constrain the redshift of the deceleration-acceleration transition, $z_{ m da}$, as well as parameters of five cosmological models: ΛCDM with curvature, flat XCDM, flat φCDM, and their non-flat counterparts. By binning data and performing likelihood analyses with two $H_0$ priors, the authors find $z_{ m da}=0.72\pm0.05$ for $H_0=68\pm2.8$ and $z_{ m da}=0.84\pm0.03$ for $H_0=73.24\pm1.74$, with $z_{ m da}$ showing limited sensitivity to the underlying model beyond $H_0$. The results are broadly consistent with flat ΛCDM but do not exclude spatial curvature or dynamical dark energy, highlighting the complementarity of $H(z)$ data with other probes and the potential for tighter constraints when combined with SNIa, BAO, growth, and CMB observations. The study demonstrates the value of an expanded $H(z)$ dataset and provides a framework for robustly inferring transition redshifts and cosmological parameters from $H(z)$ measurements alone and in joint analyses.

Abstract

We compile an updated list of 38 measurements of the Hubble parameter $H(z)$ between redshifts $0.07 \leq z \leq 2.36$ and use them to place constraints on model parameters of constant and time-varying dark energy cosmological models, both spatially flat and curved. We use five models to measure the redshift of the cosmological deceleration-acceleration transition, $z_{\rm da}$, from these $H(z)$ data. Within the error bars, the measured $z_{\rm da}$ are insensitive to the model used, depending only on the value assumed for the Hubble constant $H_0$. The weighted mean of our measurements is $z_{\rm da} = 0.72 \pm 0.05\ (0.84 \pm 0.03)$ for $H_0 = 68 \pm 2.8\ (73.24 \pm 1.74)$ km s$^{-1}$ Mpc$^{-1}$ and should provide a reasonably model-independent estimate of this cosmological parameter. The $H(z)$ data are consistent with the standard spatially-flat $Λ$CDM cosmological model but do not rule out non-flat models or dynamical dark energy models.

Hubble parameter measurement constraints on the redshift of the deceleration-acceleration transition, dynamical dark energy, and space curvature

TL;DR

This work updates the data compilation to 38 measurements spanning and uses them to constrain the redshift of the deceleration-acceleration transition, , as well as parameters of five cosmological models: ΛCDM with curvature, flat XCDM, flat φCDM, and their non-flat counterparts. By binning data and performing likelihood analyses with two priors, the authors find for and for , with showing limited sensitivity to the underlying model beyond . The results are broadly consistent with flat ΛCDM but do not exclude spatial curvature or dynamical dark energy, highlighting the complementarity of data with other probes and the potential for tighter constraints when combined with SNIa, BAO, growth, and CMB observations. The study demonstrates the value of an expanded dataset and provides a framework for robustly inferring transition redshifts and cosmological parameters from measurements alone and in joint analyses.

Abstract

We compile an updated list of 38 measurements of the Hubble parameter between redshifts and use them to place constraints on model parameters of constant and time-varying dark energy cosmological models, both spatially flat and curved. We use five models to measure the redshift of the cosmological deceleration-acceleration transition, , from these data. Within the error bars, the measured are insensitive to the model used, depending only on the value assumed for the Hubble constant . The weighted mean of our measurements is for km s Mpc and should provide a reasonably model-independent estimate of this cosmological parameter. The data are consistent with the standard spatially-flat CDM cosmological model but do not rule out non-flat models or dynamical dark energy models.

Paper Structure

This paper contains 7 sections, 18 equations, 4 figures, 7 tables.

Table of Contents

  1. Introduction
  2. New Hubble parameter data compilation
  3. Binning of Hubble parameter data
  4. Cosmological Models
  5. Cosmological deceleration-acceleration transition redshift
  6. Cosmological parameter constraints
  7. Conclusion

Figures (4)

  • Figure 1: The top panel shows the 38 $H(z)$ measurements of Table \ref{['table:Hzdata']}. All error bars are 1$\sigma$. The left (right) panel in the second row shows the binned $H(z)$ data with 3 or 4 (4 or 5) measurements per bin, combined using weighted mean statistics, listed in Table \ref{['table:WM']}. In the last row, the left (right) panel shows binned $H(z)$ data with 5 or 7 (4, 5, or 6) measurements per bin, combined using weighted mean statistics, listed in Table \ref{['table:WM']}. In all panels, there are five different colored solid (dot-dashed) best-fit model prediction lines for the two $H_0$ priors used in our analyses (see main text for details; NF stands for non-flat).
  • Figure 2: The three panels (from left to right) show $1\sigma$, $2\sigma$, and $3\sigma$ red solid (blue dot-dashed) constraint contours for the lower (higher) $H_0$ prior, for $\Lambda$CDM, flat XCDM, and flat $\phi$CDM respectively. Red solid (blue empty) circles are the best-fit points for the lower (higher) $H_0$ prior. The straight dashed lines in the first and second panels correspond to spatially-flat $\Lambda$CDM models, the dotted lines demarcate zero-acceleration models, and the shaded area in the upper left-hand corner of the left panel is the region for which there is no big bang. For quantitative parameter best-fit values and ranges see Tables \ref{['table:Un-binned data zda']} and \ref{['table:1Dfor2parametermodels']}.
  • Figure 3: The three panels (from left to right) show $1\sigma$, $2\sigma$, and $3\sigma$ two-dimensional constraint contours for the three-parameter, non-flat XCDM parameterization, computed after marginalizing over each of the three parameters in turn. Red (blue) solid lines are for the lower (higher) $H_0$ prior. Left, center, and right panels correspond to marginalizing over $\Omega_{K0}$, $\omega_X$, and $\Omega_{m0}$ respectively. Red (blue) solid circles are the best-fit points for the lower (higher) $H_0$ prior. Red (blue) dot-dashed lines in the left panel are $1\sigma$, $2\sigma$, and $3\sigma$ constraint contours for the lower (higher) $H_0$ prior for spatially-flat XCDM (see the central panel of Fig. \ref{['fig:Flatmodelsconstraints']}). For quantitative parameter best-fit values and ranges see Tables \ref{['table:Un-binned data zda']}, \ref{['table:Nonflatmodels']}, and \ref{['table:1Dfor3parametermodels']}.
  • Figure 4: The three panels (from left to right) show $1\sigma$, $2\sigma$, and $3\sigma$ two-dimensional constraint contours for the three-parameter, non-flat $\phi$CDM model, computed after marginalizing over each of the three parameters in turn. Red (blue) solid lines are for the lower (higher) $H_{0}$ prior. Left, center, and right panels correspond to marginalizing over $\Omega_{K0}$, $\alpha$, and $\Omega_{m0}$ respectively. Red (blue) solid circles are the best-fit points for the lower (higher) $H_{0}$ prior. Red (blue) dot-dashed lines in the left panel are $1\sigma$, $2\sigma$, and $3\sigma$ constraint contours for the lower (higher) $H_0$ prior for the spatially-flat $\phi$CDM model (see the right panel of Fig. \ref{['fig:Flatmodelsconstraints']}). For quantitative parameter best-fit values and ranges see Tables \ref{['table:Un-binned data zda']}, \ref{['table:Nonflatmodels']}, and \ref{['table:1Dfor3parametermodels']}.