Development of Zeldovich's approach for cosmological distances measurement in the Friedmann Universe

TL;DR

This paper develops a generalized differential equation for measuring the angular diameter distance in Friedmann universes, accounting for various cosmological parameters and matter-energy contents, and demonstrates its numerical solutions.

Contribution

It derives a universal differential equation for the angular diameter distance applicable to all Friedmann universe models, including numerical solutions for different matter-energy compositions.

Findings

Strong dependence of ADD on the filling of the cone of light rays

Difference between empty and filled cones can reach 600-700 Mpc at redshift ~3

Equation suitable for numerical investigations of cosmological distances

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 $f\simeq 3$.