Interactivation and cosmological parameters

The study begins as an essay of epistemology on cosmological concepts from antiquity to present time with special attention to the evolution of mentalities in cosmological research and to observational tests of comological models. Among them, the significance of the relation between angular diameter $\theta$ and {\it distance} (today {\it cosmological redshift $z_c$}) is the leading idea. \\ The aim of constraining $\Omega_{m\circ}$ and $\Omega_{\Lambda\circ}$, the present rates of the density cosmological parameters for a Friedmann-Lema\^{\i}tre universe, with observation of the $\theta \longleftrightarrow z_c$ relation of binary objects has driven, for more than twenty years, a set of observational activities ranging from dedicated pointings (imagery, spectrophotometry 1D, 2D or 3D) to wide field astronomy (astrometry, photometry, proper motions).\\ The distribution of linear separations between two interacting ({\it ``interactivating''}) galaxies, when both of them undergo a {\it primary starburst}, is used as a standard of length. \\ The qualification of that method is performed with analysis of available surveys of galaxies. Statistical properties of the linear separations of such pairs of {\it interacti\-vated} galaxies are estimated from low redshift real data. Synthetic samples are generated and the resolution of the inverse problem provides the probability densities of the retrieved cosmological parameters. The accuracies that can be achieved by that method on $\Omega_{m\circ}$ and $\Omega_{\Lambda\circ}$ are computed depending on the size of ongoing real samples.