Hubble tension and absolute constraints on the local Hubble parameter.

Abstract

It is shown that, from the two independent approaches of McCrea-Milne and of Zeldovich, one can fully recover the set equations corresponding to relativistic equations of the expanding universe of Friedmann-Lemaitre-Robertson-Walker geometry. Although similar, the Newtonian and relativistic set of equations, have principal difference in the content and hence define two flows, local and global ones, thus naturally exposing the Hubble tension at presence of the cosmological constant \Lambda. From that, 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.