On the relationship between mean observations, spatial averages and the Dyer-Roeder approximation in Einstein-Straus models
Abstract
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.
Keywords
Cite
@article{arxiv.2010.04500,
title = {On the relationship between mean observations, spatial averages and the Dyer-Roeder approximation in Einstein-Straus models},
author = {S. M. Koksbang},
journal= {arXiv preprint arXiv:2010.04500},
year = {2021}
}
Comments
23 pages plus references, 8 captioned figures. Accepted for publication in JCAP.v2: Typos in eq. 1.1 and 1.2 fixed. 1 reference added (to match published version)