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

Abstract

The universe, with large-scale homogeneity, 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 take consideration of the inhomogeneities in 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 Ω M , the state of dark energy ω, and the smoothnessparameter α are constrained by a set of OHD in a spatially flat ΛCDM universe as well as a spatially flat XCDM universe. By using of χ 2 minimization method we get α = 0.81 +0.19 −0.20 and Ω M = 0.32 +0.12 −0.06 at 1σ confidence level. If we assume a Gaussian prior of Ω M = 0.26 ± 0.1, we get α = 0.93 +0.07 −0.19 and Ω M = 0.31 +0.06 −0.05 . For XCDM model, α is constrained to α ≥ 0.80 but ω is weakly constrained around -1, where ω describes the equation of the state of the dark energy (p X = ωρ X ). We conclude that OHD constrains the smoothness parameter more effectively than the data of SNe Ia and compact radio sources.

Constraining smoothness parameter and the DD relation of Dyer-Roeder equation with supernovae

“…Santos et al [7] used the 182 SNe Ia data of Riess et al [8] to obtain that α ≥ 0.42 (2σ). Yu et al [9] got α = 0.81 +0. 19 −0.20 at 1σ CL via the observational H(z) data, and Busti et al [10] got α ≥ 0.25 (2σ) using Union2 SNe Ia data.…”

Them–zrelation for Type Ia supernovae: safety in numbers or safely without worry?

“…Note that Yu et al (2011), using observational data other than the m-z relation for Type Ia supernovae, and assuming a flat Universe, arrive at essentially the same conclusion as Helbig (2015): η ≈ 1 is favoured and low values of η can be ruled out. 3 Some of the assumptions in Yu et al (2011) were questioned by Busti & Santos (2011), but even when these are corrected for, η ≈ 1 is still favoured.…”

Calculation of distances in cosmological models with small-scale inhomogeneities and their use in observational cosmology: a review

“…using supernova data, concluding that η > 0.42 (2σ). Adding the H(z) data used by Yu et al (2011) of course improves the constraints, resulting in 0.66 ≤ η ≤ 1.0 (2σ) with the best fit at η = 1, a broadly similar result. Note that Helbig (2015a) also finds the best-fit value η = 1 if λ 0 and/or Ω 0 are constrained.…”

“…In an interesting but somewhat confusingly written paper, Yu et al (2011) use the m-z relation and the angular-size-redshift relation (based on data from the literature) to determine Ω 0 and η in flat cosmological models (and the equation-of-state parameter w-confusingly referred to as ω-and η for flat models with Ω 0 = 0.28). Of course, H is in general a function of z, but this is not something which is measured directly.…”