Einstein universes stabilized

TL;DR

This paper explores how gravitational self-binding energy can stabilize Einstein universes, showing that certain geometric and parameter conditions lead to a self-sustaining, stable cosmological model.

Contribution

It introduces a Newtonian and Weyl geometric framework demonstrating conditions for the stability of Einstein universes based on gravitational self-binding energy.

Findings

Spherical spaces can be stabilized by gravitational self-binding energy.

Weyl geometric Einstein universes are stable under specific curvature and parameter conditions.

Stability depends on the self energy coefficient ta, which varies with geometry.

Abstract

The hypothesis that gravitational self-binding energy may be the source for the vacuum energy term of cosmology is studied in a Newtonian Ansatz. For spherical spaces the attractive force of gravitation and the negative pressure of the vacuum energy term form a self stabilizing system under very reasonable restrictions for the parameters, among them a characteristic coefficient \beta of self energy. In the Weyl geometric approach to cosmological redshift, Einstein-Weyl universes with observational restrictions of the curvature parameters are dynamically stable, if \beta is about 40 % smaller than in the exact Newton Ansatz or if the space geometry is elliptical.