Eternal expansion of closed universe

TL;DR

This paper analyzes the conditions under which a closed universe can expand forever, exploring potential barriers, phase-space dynamics, and the implications of cosmological parameters for eternal expansion.

Contribution

It provides a detailed phase-space analysis and conditions for eternal expansion of a closed universe, including potential barriers and restrictions on cosmological parameters.

Findings

Conditions for overcoming the potential barrier in closed universe expansion

Phase-space trajectories indicating eternal expansion

Restrictions on Friedmann integrals and cosmological constants

Abstract

The expansion of the closed two-component universe has been considered. The potential barrier of the expansion has been investigated and its overcoming condition has been obtained. The restrictions on the Friedmann integrals, cosmological constant and density parameters have been analyzed. The phase-space has been considered and the phase curves of eternally expanding closed universes have been plotted. A questionable coincidence of the our Universe Friedmann integrals has been discussed.