On the Stability of Fundamental Couplings in the Galaxy

Astrophysical tests of the stability of Nature's fundamental couplings are a key probe of the standard paradigms in fundamental physics and cosmology. In this report we discuss updated constraints on the stability of the fine-structure constant $\alpha$ and the proton-to-electron mass ratio $\mu=m_p/m_e$ within the Galaxy. We revisit and improve upon the analysis by Truppe {\it et al.} by allowing for the possibility of simultaneous variations of both couplings and also by combining them with the recent measurements by Levshakov {\it et al.} By considering representative unification scenarios we find no evidence for variations of $\alpha$ at the 0.4 ppm level, and of $\mu$ at the 0.6 ppm level; if one uses the Levshakov bound on $\mu$ as a prior, the$\alpha$ bound is improved to 0.1 ppm. We also highlight how these measurements can constrain (and discriminate among) several fundamental physics paradigms.