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

In this Comment we discuss a recent analysis by Yu et al. [RAA 11, 125 (2011)] about constraints on the smoothness $α$ 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 $α$ parameter, a $χ^2$-test involving a sample of SNe Ia and $H(z)$ data in the context of a flat $Λ$CDM model is reanalyzed. This result is confronted with an earlier approach discussed by Santos et al. (2008) without $H(z)$ data. In the ($Ω_m, α$) plane, it is found that such parameters are now restricted on the intervals $0.66 \leq α\leq 1.0$ and $0.27 \leq Ω_m \leq 0.37$ within 95.4% confidence level (2$σ$), 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 $Ω_m$.