The Age of the Universe with Globular Clusters III: Gaia distances and hierarchical modeling

This is the third article in a series aimed at computing accurate and precise ages of galactic globular clusters from their full color-magnitude diagram in order to estimate the age of the Universe and in turn constrain the cosmological model. We update previous constraints using additional data and an improved methodology which allows us to vary the helium abundance and the reddening law in addition to the usual parameters (age, metallicity, alpha enhancement, distance and absorption) in the analysis. Even with the additional degrees of freedom, using the full color-magnitude diagram, now described as a Gaussian mixture Bayesian hierarchical model, a tight constraint on the age(s) of the globular clusters and on the other parameters can be obtained, and the statistical errors are fully subdominant to the systematic errors. We find that the age of the oldest globular clusters is $t_{\rm GC} = 13.39 \pm 0.10 ({\rm stat.}) \pm 0.23 ({\rm sys.})$ Gyr, resulting in an age of the Universe $t_{\rm U}=13.57^{+ 0.16}_{-0.14} ({\rm stat})\pm 0.23 ({\rm sys.})$ and a robust 95\% confidence upper limit of $t_U^{\leq}=13.92_{-0.1}^{+0.13}({\rm stat}) \pm{0.23} ({\rm sys})$. This is fully compatible with our previous estimates and with the model-dependent, Cosmic Microwave Background-derived age for the Universe of $t_{\rm U} =13.8 \pm 0.02$ Gyr for a $\Lambda$CDM model.