约束光滑参数与带超新星的Dyer-Roeder方程的DD关系
Constraining smoothness parameter and the DD relation of Dyer-Roeder equation with supernovae
摘要：
我们的真实宇宙是局部不均匀的。Dyer和Roeder引入了光滑性参数$α$来描述局域非均匀性对角直径距离的影响，得到了局域非均匀宇宙的角直径距离-红移近似关系（Dyer-Roeder方程）。此外，距离-对偶（DD）关系，$D_L(z)(1+z)^{-2}/D_A(z)=1$，应该对所有由黎曼几何描述的宇宙学模型有效，其中$D_L$和$D_A$分别是光度和角距离。因此，有必要检验Dyer-Roeder近似方程是否满足距离-对偶关系。本文利用Union2.1 SNe Ia数据约束光滑性参数$α$，检验Dyer-Roeder方程是否满足DD关系。利用$χ^2$最小化方法，我们得到了$1σ$上的$α=0.92_{-0.32}^{+0.08}$和$2σ$上的$0.92_{-0.65}^{+0.08}$，结果表明Dyer-Roeder方程与$1σ$上的DD关系具有很好的一致性.
英文摘要：
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, $D_L(z)(1+z)^{-2}/D_A(z)=1$, 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 $α=0.92_{-0.32}^{+0.08}$ at $1σ$ and $0.92_{-0.65}^{+0.08}$ at $2σ$, and our results show that the Dyer-Roeder equation is in good consistency with the DD relation at $1σ$.
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