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

Abstract

Abstract. Our real universe is locally inhomogeneous. Dyer and Roeder introduced the smoothness parameter α to describe the influence of local inhomogeneity on angular diameter distance, and they obtained the angular diameter distance-redshift approximate relation (Dyer-Roeder equation) for locally inhomogeneous universe. Furthermore, the DistanceDuality (DD) relation, D L (z)(1 + z) −2 /D A (z) = 1, should be valid for all cosmological models that are described by Riemannian geometry, where D L and D A are, respectively, the luminosity and angular distance distances. Therefore, it is necessary to test whether if the Dyer-Roeder approximate equation can satisfy the Distance-Duality relation. In this paper, we use Union2.1 SNe Ia data to constrain the smoothness parameter α and test whether the Dyer-Roeder equation satisfies the DD relation. By using χ 2 minimization, we get α = 0.92 +0.08 −0.32 at 1σ and 0.92 +0.08 −0.65 at 2σ, and our results show that the Dyer-Roeder equation is in good consistency with the DD relation at 1σ.

The effect of inhomogeneities on dark energy constraints

“…For a background concordance cosmology (i.e. w = −1), we confirm previous analyses [42,69] that find η = 0.81 ± 0.33 at the 68% C.L. However, we stress that we do not a priori fix the cosmological parameter values as in [42], but rather we constrain it with data complementary to SN Ia distances.…”

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

“…(While no useful constraints are possible, the global maximum likelihood in the λ 0 -Ω 0 -η cube also indicates a high value of η.) Unknown to me at the time, very similar results, based on the same data, were obtained by Yang et al (2013), Bréton & Montiel (2013), and, somewhat later, Li et al (2015) (the latter two restricted to a flat universe). While perhaps not surprising, it is of course important in science for results to be confirmed by others working independently.…”

“…Busti et al (2013) compared the ZKDR distance to other approximations: the weak-lensing approximation with uncompensated density along the line of sight, the flux-averaging approximation, and a modified ZKDR distance which allows for a different expansion rate along the line of sight. This work is interesting for its analysis of the underlying issues (essentially assumptions about the mass distribution and how this affects light propagation, different approximations corresponding to different assumptions) and its combination of detailed theory and application to real data-the Union2.1 sample, also used by Helbig (2015a) and Yang et al (2013). 13.…”

Constraints on the cosmic distance duality relation with simulated data of gravitational waves from the Einstein Telescope

“…The ideal way to observationally test the CDDR is via independent measurements of intrinsic luminosities and sizes of the same object, without using a specific cosmological model [35]. We may quote approaches involving: measurements of the angular diameter distance (ADD) of galaxy clusters, observations of SNe Ia, estimates of the cosmic expansion H(z) from cosmic chronometers, measurements of the gas mass fraction in galaxy clusters and observations of strong gravitational lensing (SGL) [36,37,38,39,40,41,42,43,44,45]. All these tests were performed using different sources for D A and D L .…”