Hubble Parameter and Baryon Acoustic Oscillation Measurement Constraints on the Hubble Constant, the Deviation from the Spatially-Flat $Λ$cdm Model, The Deceleration-Acceleration Transition Redshift, and Spatial Curvature (1711.03437v2)

Abstract: We compile a complete collection of reliable Hubble parameter $H(z)$ data to redshift $z \leq 2.36$ and use them with the Gaussian Process method to determine continuous $H(z)$ functions for various data subsets. From these continuous $H(z)$'s, summarizing across the data subsets considered, we find $H_0\sim 67 \pm 4\,\rm km/s/Mpc$, more consistent with the recent lower values determined using a variety of techniques. In most data subsets, we see a cosmological deceleration-acceleration transition at 2$\sigma$ significance, with the data subsets transition redshifts varying over $0.33<z_{\rm da}<1.0$ at 1$\sigma$ significance. We find that the flat-$\Lambda$CDM model is consistent with the $H(z)$ data to a $z$ of 1.5 to 2.0, depending on data subset considered, with 2$\sigma$ deviations from flat-$\Lambda$CDM above this redshift range. Using the continuous $H(z)$ with baryon acoustic oscillation distance-redshift observations, we constrain the current spatial curvature density parameter to be $\Omega_{K0}=-0.03\pm0.21$, consistent with a flat universe, but the large error bar does not rule out small values of spatial curvature that are now under debate.

• The paper employs the Gaussian Process method on 36 Hubble parameter (H(z)) and BAO data points to generate continuous H(z) functions and derive cosmological constraints.
• Analysis yields a Hubble constant (H0) around 67 1 4 km/s/Mpc and identifies the deceleration-acceleration transition redshift (z_da) within 0.33 < z_da < 1.0.
• The study finds consistency with the flat-$blambda$CDM model up to z=2.0 but tentative deviations above this redshift, constraining spatial curvature consistent with flat.

Insights on the Constraints of the Hubble Parameter and Cosmological Measurements

The paper by Hai Yu, Bharat Ratra, and Fa-Yin Wang makes significant contributions to the ongoing efforts to refine our understanding of cosmological parameters, particularly focusing on the Hubble constant $H_0$, the transition of cosmic deceleration to acceleration, the deviation from the spatially flat $\Lambda$CDM model, and constraints on spatial curvature. This paper, leveraging a comprehensive set of currently available, reliable Hubble parameter $H(z)$ data, employs the Gaussian Process (GP) method to generate continuous functions of $H(z)$ and derive insights into the underpinnings of cosmic expansion.

The researchers meticulously compiled 36 $H(z)$ data points spanning redshifts $0.07 \leq z \leq 2.36$. The dataset combines 31 measurements from cosmic chronometry and 5 from baryon acoustic oscillation (BAO) techniques, effectively enhancing the scope and depth of the analysis. Through the adoption of the GP method, the paper refines these discrete $H(z)$ measurements into smooth, continuous functions, allowing for a more nuanced extraction of cosmological parameters.

Key Findings

1. Hubble Constant, $H_0$: Averaging across 12 distinct $H(z)$ data samples—each varying by data inclusiveness and assumptions regarding $H_0$—the paper estimates $H_0$ around $67 \, \pm 4 \, \text{km/s/Mpc}$. This value aligns more closely with recent measurements indicating lower $H_0$ values, although the significant error margins encompass higher local measurements as well.
2. Deceleration-Acceleration Transition, $z_{\rm da}$: The research highlights a significant cosmological deceleration-acceleration transition, identified within the 1$\sigma$ redshift range of $0.33 < z_{\rm da} < 1.0$. The identified range is broader compared to those obtained via cosmological model templates, pointing to the GP method's flexibility in accommodating variation within data.
3. Testing Flat-$\Lambda$CDM Model: Within a redshift range extending up to 2.0, depending on the selected data sample, the flat-$\Lambda$CDM model remains consistent with $H(z)$ data. However, above this redshift, deviations appear—albeit at a tentative 2$\sigma$ significance. As the data quality at higher redshifts improves, this preliminary finding may provide crucial insights into potential modifications of the $\Lambda$CDM model.
4. Spatial Curvature, $\Omega_{K0}$: By integrating $H(z)$ with BAO data, the paper constrains the current spatial curvature density parameter to $\Omega_{K0} = -0.03 \pm 0.21$. While consistent with a flat universe, the large error bars present do not exclude the possibility of minor spatial curvature that has been debated in other studies.

Implications and Future Directions

The implications of these findings are manifold. Firstly, the alignment of $H_0$ with lower contemporary values reinforces certain cosmological observations over more traditionally accepted higher ones. Secondly, the deceleration-acceleration transition's broad range necessitates deeper investigations, as it might signify alternative dynamics to the dark energy or underlying assumptions of the standard model. Thirdly, the potential divergence from the flat-$\Lambda$CDM model at higher redshifts invites further cosmological probes into its validity or the necessity for adjustments.

Looking forward, upcoming high-precision $H(z)$ data and improvements in BAO measurements will be instrumental in refining these constraints and resolving current ambiguities. Future research endeavours might also explore the potential for other models to depict the cosmological dynamics more accurately, especially those that can incorporate slight spatial curvature while still remaining congruous with empirical data.

In summary, this comprehensive examination of $H(z)$ data, demonstrating effective methodological application through the GP method, provides pertinent contributions to our comprehension of large-scale cosmic dynamics and the parameters that govern them. The paper ultimately sets a solid foundation for subsequent studies targeting further precision and model refinement within the field of cosmology.