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

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 $\Lambda$CDM cosmological model but do not rule out non-flat models or dynamical dark energy models.

• The paper establishes a model-independent deceleration-acceleration transition redshift of z_da = 0.72 ± 0.05 based on H(z) data.
• It utilizes an updated set of 38 H(z) measurements across redshifts 0.07 to 2.36 to compare constant and dynamic dark energy models with varying curvature.
• The analysis reaffirms the spatially-flat ΛCDM model while emphasizing the need for refined high-redshift observations to resolve H0 tensions.

Constraints on Cosmological Parameters Using Hubble Parameter Data

Overview

The paper by Farooq et al. addresses the utilization of Hubble parameter $H(z)$ measurements to place constraints on cosmological models featuring constant and dynamic dark energy and varying spatial curvature. An updated compilation of 38 $H(z)$ measurements spanning redshifts from $z = 0.07$ to $z = 2.36$ is used for this purpose. The analysis is based on five different cosmological models to determine the redshift $z_{\rm da}$ of the transition from cosmological deceleration to acceleration. The objective is to assess the consistency of the $H(z)$ data with the standard $\Lambda$CDM model and to explore the viability of models allowing for spatial curvature and dynamic dark energy.

Implications of the Study

The paper's findings support the concordance model of cosmology, displaying $z_{\rm da}$ values that align well with the spatially-flat $\Lambda$CDM model. Specifically, for $H_0 = 68 \pm 2.8$, a calculated $z_{\rm da} = 0.72 \pm 0.05$ suggests a largely model-independent estimation of this transition, consistent across various cosmological scenarios. However, the analysis does not firmly exclude models with non-flat geometries or those with dynamic dark energy, exemplifying the persistent uncertainties and debates surrounding precise cosmological parameters.

Numerical Findings and Constraints

The $H(z)$ dataset supports an average deceleration-acceleration transition redshift $z_{\rm da}$ consistent with other cosmological measurements such as BAO and CMB anisotropies. This consistency reaffirms the robustness of the standard model's parameters but highlights the sensitivity of results to $H_0$. Notably, the envelope of $H(z)$ data allows for estimates of other cosmological parameters (e.g., $\Omega_{m0}$), with constraints that are tighter than those from individual datasets, though still broader than those obtainable from combined analyses including other data types.

Future Computational and Observational Directions

The analysis implies that forthcoming precision measurements of $H(z)$, especially at higher redshifts and with improved accuracy, have the potential to refine these constraints further. As the data are consistent with $\Lambda$CDM but open to alternative cosmological paradigms, future research should focus on integrating growing astronomical datasets from both traditional and novel observational avenues to disentangle the degeneracies between dark energy behavior and space curvature. Additionally, these developments might provide insight into the persistent tension in $H_0$ measurements, which remains an intriguing anomaly in modern cosmological inquiries.

In summary, while the current analysis corroborates the spatially-flat $\Lambda$CDM model, it signifies the necessity for continued examination of local and high-redshift universe's expansion dynamics. By bridging observational data and theoretical models, future studies will be crucial in the progressive refinement of cosmological parameters defining our universe.