2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99696In 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.8 pages, LaTeX; minor layout changes, typos corrected, one new equation, new reference [5], completed reference [13], two references addedGeneral Relativity and Quantum CosmologyAstrophysicsHigh Energy Physics - Theorytext