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

We discuss a recent analysis by Yu et al. [RAA 11, 125 (2011)] about constraints on the smoothness parameter alpha 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 parameter alpha, a chi(2)-test involving a sample of type Ia supernovae and H(z) data in the context of a flat ACDM 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 to be in the intervals 0.66 <= alpha <= 1.0 and 0.27 <= Omega(m) <= 0.37 within the 95.4% confidence level (2 sigma), and, therefore, are 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).