On astrophysical bounds of the cosmological constant

TL;DR

This paper investigates astrophysical constraints on the cosmological constant for spherical bodies, showing that bounds derived from both relativistic and Newtonian frameworks are consistent and comparable.

Contribution

It demonstrates that bounds on the cosmological constant from exact solutions are not exclusive to relativistic theory but also appear in Newtonian physics, and compares different inequalities related to these bounds.

Findings

Bounds from exact solutions are not unique to relativistic theory.

Newtonian and relativistic bounds on the cosmological constant are similar.

Different inequalities related to bounds are compared and analyzed.

Abstract

Astrophysical bounds on the cosmological constant are examined for spherically symmetric bodies. Similar limits emerge from hydrostatical and gravitational equilibrium and the validity of the Newtonian limit. It is argued that the bound coming from the analysis of exact solutions is not a feature of the relativistic theory since it also emerges from the Newtonian theory. The methods in use seem to be disjoint from the basic principles, however they have the same implication regarding the upper bounds. Therefore we will compare different inequalities and comment on the possible relationship between them.