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

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 these 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 we show the strong dependence ADD has 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 a redshift of f≃3.