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Abstract: The distance-redshift relation plays an important role in cosmology. In thestandard approach to cosmology it is assumed that this relation is the same asin the homogeneous universe. As the real universe is not homogeneous there areseveral methods to calculate the correction. The weak lensing approximation andthe Dyer-Roeder relation are one of them. This paper establishes a link betweenthese two approximations. It is shown that if the universe is homogeneous withonly small, vanishing after averaging, density fluctuations along the line ofsight, then the distance correction is negligible. It is also shown that avanishing 3D average of density fluctuations does not imply that the mean ofdensity fluctuations along the line of sight is zero. In this case, even withinthe linear approximation, the distance correction is not negligible. Themodified version of the Dyer-Roeder relation is presented and it is shown thatthis modified relation is consistent with the correction obtained within theweak lensing approximation. The correction to the distance for a source at z ~2 is of order of a few percent. Thus, with an increasing precision ofcosmological observations an accurate estimation of the distance is essential.Otherwise errors due to miscalculation the distance can become a major sourceof systematics.



Author: Krzysztof Bolejko

Source: https://arxiv.org/







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