Constraints on the general solutions of Einstein cosmological equations by Hubble parameter times cosmic age: a historical perspective

TL;DR

This paper explores solutions to Einstein's cosmological equations using recent observational data on the Hubble parameter and universe age, analyzing their implications for different cosmological models.

Contribution

It provides a historical perspective on compact solutions of Einstein's equations incorporating the cosmological constant and curvature, constrained by recent observational estimates.

Findings

KOFL solutions align with high-redshift galaxy observations

ΛCDM solutions face reconciliation challenges

Quantitative analysis of different cosmological models

Abstract

In a historical perspective, compact solutions of Einstein's equations, including the cosmological constant and the curvature terms, are obtained, starting from two recent observational estimates of the Hubble's parameter (H0) and the "age" of the universe (t0). Cosmological implications for {\Lambda}CDM ({\Lambda} Cold Dark Matter), KOFL (k Open Friedman-Lemaitre), plus two mixed solutions are investigated, under the constraints imposed by the relatively narrow current uncertainties. Quantitative results obtained for the KOFL case seem to be compatible with matter density and the highest observed red-shifts from distant galaxies, while those obtained for the {\Lambda}CDM may be more difficult to reconcile.