Abstract
We present our development of Zeldovich's ideas for the measurement of the cosmological angular diameter distance (ADD) in the Friedmann Universe. We derive the general differential equation for the ADD measurement which is valid for an open, spatially-flat and closed universe, and for any stress energy tensor. We solve the mentioned equations in terms of quadratures in a form suitable for further numerical investigations for the present universe filled by radiation, (baryonic and dark) matter and dark energy. We perform the numerical investigation in the absence of radiation, and show the strong dependence ADD on the filling of the cone of light rays (CLR). The difference of the empty and totally filled CLR may reach 600-700 Mps. for the redshift $f\simeq 3$.
Highlights
In the present article, we are going to reconsider the issue of cosmological distances measurement in cosmology
The paper is organized as follows: in Sect. 2 we present the general approach for the angular diameter distance (ADD) measurement in the Friedmann Universe and we derive the equation for the evolution of the cross-section diameter z of a light beam from a distant object
We extended Zeldovich’s ideas for ADD measurements in two directions
Summary
We are going to reconsider the issue of cosmological distances measurement in cosmology. In the article [5] Zeldovich introduced “a homogeneous in the mean universe“ and he analyzed the effect of the local non-uniformity of the matterdominated spatially flat Friedmann Universe on the angular and luminosity distances measurement It was found for the ADD under suggestion that there was a negligible amount of matter inside the light cone and it was possible to neglect the gravitational effect of that matter. It is well known that for ADD measurements a very small angle (of a few arc seconds) should be considered For this reason, we cannot say anything about a homogeneous and isotropic universe in this thin cone of light rays and the use of the FLRW metric is questionable in this case.
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