Hubble tension and absolute constraints on the local Hubble parameter

Abstract: It is shown, from the two independent approaches of McCrea-Milne and of Zeldovich, that one can fully recover the set equations corresponding to the relativistic equations of the expanding universe of Friedmann-Lemaitre-Robertson-Walker geometry. Although similar, the Newtonian and relativistic set of equations have a principal difference in the content and hence define two flows, local and global ones, thus naturally exposing the Hubble tension at the presence of the cosmological constant \Lambda. From this, we obtain absolute constraints on the lower and upper values for the local Hubble parameter, \sqrt{\Lambda c^2/3} \simeq 56.2$ and \sqrt{\Lambda c^2} \simeq 97.3 (km/sec Mpc^{-1}), respectively. The link to the so-called maximum force--tension issue in cosmological models is revealed.