Comment on "Constraining the smoothness parameter and dark energy using observational H(z) data"

TL;DR

This paper critiques a recent analysis on dark energy constraints using H(z) data, reanalyzes the data with a proper statistical approach, and finds that H(z) data mainly tighten matter density constraints, supporting the homogeneous universe model.

Contribution

It clarifies the proper methodology for analyzing H(z) data in the context of the Dyer-Roeder approach and updates constraints on the smoothness parameter and matter density.

Findings

H(z) data restricts the smoothness parameter to 0.66-1.0 at 95.4% confidence

H(z) data primarily tighten constraints on the matter density parameter Ω_m

Results are consistent with a homogeneous universe (α=1)

Abstract

In this Comment we discuss a recent analysis by Yu et al. [RAA 11, 125 (2011)] about constraints on the smoothness $\alpha$ parameter and dark energy models using observational $H(z)$ data. It is argued here that their procedure is conceptually inconsistent with the basic assumptions underlying the adopted Dyer-Roeder approach. In order to properly quantify the influence of the $H(z)$ data on the smoothness $\alpha$ parameter, a $\chi^2$-test involving a sample of SNe Ia and $H(z)$ data in the context of a flat $\Lambda$CDM model is reanalyzed. This result is confronted with an earlier approach discussed by Santos et al. (2008) without $H(z)$ data. In the ($\Omega_m, \alpha$) plane, it is found that such parameters are now restricted on the intervals $0.66 \leq \alpha \leq 1.0$ and $0.27 \leq \Omega_m \leq 0.37$ within 95.4% confidence level (2$\sigma$), and, therefore, fully compatible with the homogeneous case. The basic conclusion is that a joint analysis involving $H(z)$ data can indirectly improve our knowledge about the influence of the inhomogeneities. However, this happens only because the $H(z)$ data provide tighter constraints on the matter density parameter $\Omega_m$.