Hubble tension and absolute constraints on the local Hubble parameter

TL;DR

This paper explores the fundamental differences between Newtonian and relativistic cosmological equations, revealing constraints on the local Hubble parameter and addressing the Hubble tension through theoretical approaches.

Contribution

It demonstrates how classical approaches can recover relativistic cosmological equations and establishes absolute bounds on the local Hubble parameter considering the cosmological constant.

Findings

Derived absolute bounds on the local Hubble parameter: approximately 56.2 and 97.3 km/sec Mpc^{-1}.

Revealed the connection between Hubble tension and maximum force-tension in cosmology.

Highlighted the distinction between local and global cosmological flows.

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.