Constraints on smoothness parameter and dark energy using observational H(z) data

With large-scale homogeneity,the universe is locally inhomogeneous,clustering into stars,galaxies and larger structures.Such property is described by the smoothness parameter α which is defined as the proportion of matter in the form of intergalactic medium.If we consider the inhomogeneities over a small scale,there should be modifications of the cosmological distances compared to a homogenous model.Dyer and Roeder developed a second-order ordinary differential equation（D-R equation） that describes the angular diameter distance-redshift relation for inhomogeneous cosmological models.Furthermore,we may obtain the D-R equation for observational H（z） data（OHD）.The density-parameter ΩM,the state of dark energy ω,and the smoothness-parameter α are constrained by a set of OHD in a spatially flat XCDM universe as well as a spatially flat XCDM universe.By using a χ2 minimization method,we get α = 0.81＋0.19-0.20 and ΩM = 0.32＋0.12-0.06 at the 1σ confidence level.If we assume a Gaussian prior of ΩM = 0.26 ± 0.1,we get α = 0.93＋0.07-0.19 and ΩM = 0.31＋0.06-0.05.For the XCDM model,α is constrained to α≥ 0.80 but ω is weakly constrained around-1,where ω describes the equation of state of the dark energy（pX = ωρX）.We conclude that OHD constrains the smoothness parameter more effectively than the data of SNe Ia and compact radio sources.