The Einstein static universe with torsion and the sign problem of the cosmological constant

TL;DR

This paper explores the Einstein static universe within Einstein-Cartan theory, incorporating torsion and spin effects, and discusses potential solutions to the cosmological constant's sign problem.

Contribution

It generalizes the Einstein static universe to include torsion in Einstein-Cartan theory and proposes a novel approach to address the cosmological constant's sign problem.

Findings

Constructed Einstein static universe with constant torsion.

Analyzed the interplay between torsion and the cosmological constant.

Suggested a possible resolution to the sign problem of the cosmological constant.

Abstract

In the field equations of Einstein-Cartan theory with cosmological constant a static spherically symmetric perfect fluid with spin density satisfying the Weyssenhoff restriction is considered. This serves as a rough model of space filled with (fermionic) dark matter. From this the Einstein static universe with constant torsion is constructed, generalising the Einstein Cosmos to Einstein-Cartan theory. The interplay between torsion and the cosmological constant is discussed. A possible way out of the cosmological constant's sign problem is suggested.