Abstract 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 inho mogeneous 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 ΛCDM 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.

Keywords cosmology — dark energy — cosmological parameters

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