Einstein-Straus模型中平均观测值、空间平均值和Dyer-Roeder近似之间的关系
On the relationship between mean observations, spatial averages and the Dyer-Roeder approximation in Einstein-Straus models
摘要：
考虑了不同爱因斯坦-斯特劳斯模型中的红移和红移-距离关系。具体而言，这些观测值沿1000光线在不同的特定模型的平均值进行比较与预测的基础上的Dyer-Roeder近似和基于空间平均的关系。结果表明，在一定的限制，包括那些在文献中研究的早期，基于空间平均的Dyer-Roeder近似和关系同意彼此的红移和红移距离的关系有很好的精度，并作出很好的预测的平均值的确切关系。在两种方法不一致的极限中，Dyer-Roeder近似显然产生更好的真实平均值近似。这是解释的边界条件和集成Sachs-Wolfe贡献的效果，但它指出，该结果似乎是有效的其他瑞士奶酪模型以及。最后，给出了爱因斯坦-斯特劳斯模型中红移漂移的表达式，并用于研究这一量在特定爱因斯坦-斯特劳斯模型中的行为。
英文摘要：
The redshift and redshift-distance relation in different Einstein-Straus models are considered. Specifically, the mean of these observables along 1000 light rays in different specific models are compared with predictions based on the Dyer-Roeder approximation and relations based on spatial averaging. It is shown that in certain limits, including those studied earlier in the literature, the Dyer-Roeder approximation and relations based on spatial averages agree with each other to a good precision regarding the redshift and redshift-distance relation and make good predictions of the mean of the exact relations. In limits where the two methods disagree, the Dyer-Roeder approximation clearly yields the better approximation of the true mean. This is explained by demonstrating the effect of boundary terms and integrated Sachs-Wolfe contributions but it is pointed out that the result seems to be valid for other Swiss-cheese models as well. Lastly, an expression for the redshift drift in Einstein-Straus models is presented and used for studying the behavior of this quantity in particular Einstein-Straus models.
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