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Time-Variation of Newton's Constant and the Age of Globular Clusters

A variation of Newton's constant $G$ over cosmological time scales would modify the main-squence time of globular cluster (GC) stars. We have calculated the evolution of low-mass stars typical for GCs both for standard non-varying $G$ and under the assumption of a linear variation of $G$. The age of the isochrones resulting from the latter models then was chosen such that the isochrones mimicked the standard ones at the turnoff. Assuming that the true age of GCs is between $8$ and $20\,\rm Gyr$, and because their apparent age is between $14$ and $18\,\rm Gyr$, we find that today $-35{\times}10^{-12}\,{\rm yr}^{-1}\la\dot{G}/G\la 7{\times}10^{-12}\,{\rm yr}^{-1}$. The upper limit (gravity weaker in the past) is competitive with direct present-day bounds from celestial mechanics. Within independently determined $\dot{G}/G$ limits a time-varying $G$ as an explanation for the discrepancy between the cosmic expansion age and the apparent GC ages is conceivable.