The Tinsley Diagram Revisited

Abstract

Motivated by the recent determinations of the Hubble constant $(H_0)$ from observations of Cepheid variables in NGC4571 and M100, we plot the Tinsley diagram with level curves of the cosmological constant $(Λ)$. Based on current estimates of the absolute ages of globular clusters we conclude that $Λ> 0$ and, irrespective of the background spatial curvature, the universe will not recollapse. These conclusions hold for both relativistic and Newtonian models and are {\it independent} of the density parameter.