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

Journal Article · Sat Jun 01 04:00:00 EDT 2013 · Journal of Cosmology and Astroparticle Physics

DOI:https://doi.org/10.1088/1475-7516/2013/06/007· OSTI ID:22282897

Yang, Xi; Yu, Hao-Ran; Zhang, Tong-Jie ^[1]

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1. Department of Astronomy, Beijing Normal University, Beijing 100875 (China)

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 Distance-Duality (DD) relation, D{sub L}(z)(1+z){sup −2}/D{sub A}(z) = 1, should be valid for all cosmological models that are described by Riemannian geometry, where D{sub L} and D{sub 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 meet the DD relation. By using χ{sup 2} minimization, we get α = 0.92{sub −0.32}{sup +0.08} at 1σ and 0.92{sub −0.65}{sup +0.08} at 2σ, and our results show that the Dyer-Roeder equation is in good consistency with the DD relation at 1σ.

• OSTI ID: 22282897
• Journal Information: Journal of Cosmology and Astroparticle Physics, Journal Name: Journal of Cosmology and Astroparticle Physics Journal Issue: 06 Vol. 2013; ISSN 1475-7516
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
APPROXIMATIONS
COSMOLOGICAL MODELS
DISTANCE
DUALITY
GEOMETRY
LUMINOSITY
RED SHIFT
RIEMANN SPACE
SMOOTH MANIFOLDS
SUPERNOVAE
UNIVERSE