Constraints on the variations of the fundamental couplings

We reconsider several current bounds on the variation of the fine-structure constant in models where all gauge and Yukawa couplings vary in an interdependent manner, as would be expected in unified theories. In particular, we reexamine the bounds established by the Oklo reactor from the resonant neutron capture cross section of ${}^{149}\mathrm{Sm}.$ By imposing variations in ${\Lambda }_{\mathrm{QCD}}$ and the quark masses, as dictated by unified theories, the corresponding bound on the variation of the fine-structure constant can be improved by about 2 orders of magnitude in such theories. In addition, we consider possible bounds on variations due to their effect on long lived α- and β-decay isotopes, particularly ${}^{147}\mathrm{Sm}$ and ${}^{187}\mathrm{Re}.$ We obtain a strong constraint on $\Delta \alpha /\alpha ,$ comparable to that of Oklo but extending to a higher redshift corresponding to the age of the solar system, from the radioactive lifetime of ${}^{187}\mathrm{Re}$ derived from meteoritic studies. We also analyze the astrophysical consequences of perturbing the decay Q values on bound state β decays operating in the s process.