Equations governing the evolution of a star involve multiple coupling constants. Thus, the time it spends as a main-sequence star can be expected to depend on whether or not such constants vary over the time scale of stellar evolution. When the star belongs to a globular cluster, the star's age cannot exceed that of the globular cluster, and the latter cannot exceed the age of the Universe. This fact can be used to constrain or verify the variation of the coupling constants, i.e., the speed of light c, the gravitational constant G, the Planck constant h, and the Boltzmann constant k. We have estimated the age of the main-sequence star analytically from the time it takes to synthesize all its hydrogen into helium under fixed and varying coupling constants scenarios. When we permitted the interrelated variation of the four constants ($G\thicksim c^{3}\thicksim h^{3}\thicksim k^{3/2}$) and differentiated between the cosmological energy and local energy conservation laws, we could show that the variation of the constants established in our earlier studies, i.e., $(\dot{G}/G)_{0}=3(\dot{c}/c)_{0}=(\dot{h}/h)_{0}=1.5 (\dot{k}/k)_{0}=5.4H_{0} =3.90(\pm 0.04)\times 10^{-10} yr^{-1}$ at the current cosmic time is consistent with the present work. Nevertheless, the challenge remains to come up with an experiment, astrometric or terrestrial, that can unequivocally prove or falsify the predicted variation.
Impact of the low solar abundance on the ages of globular clusters
本文介绍了Asplund及其合作者（2004）关于低太阳丰度对基于等时线拟合的最古老星团年龄的影响的研究结果。我们已经建立了新的恒星模型和相应的等时线使用这种新的太阳混合适当的太阳校准。我们发现使用Asplund et al.（2004）的金属丰度会导致银河系中老球状星团的典型年龄大约增加10%。虽然这可能看起来很小，但它对解释银河系球状星团的形成时代有重要影响。Asplund等人（2004）的丰度可能不一定会威胁到目前的和谐宇宙学，但会表明银河系球状星团在再电离之前和主星系体开始形成之前形成。这与目前对星系形成的理解形成对比。
The Age of the Universe with Globular Clusters IV: Multiple Stellar Populations
Berkeley Center for Cosmological Physics and Department of Physics, University of California, Berkeley（加州大学伯克利分校）；ICC, University of Barcelona（巴塞罗那大学）；ICREA（加泰罗尼亚高级研究学院）；Dipartimento di Fisica e Astronomia “Augusto Righi Università di Bologna（博洛尼亚大学）；INAF - Osservatorio di Astrofisica e Scienza dello Spazio di Bologna（意大利国家天体物理研究所波洛尼亚天文与空间科学观测站）；Lawrence Berkeley National Lab（劳伦斯伯克利国家实验室）
