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 et al . ( ) by allowing for the possibility of simultaneous variations of both couplings and also by combining them with the recent measurements by Levshakov 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 ( ) 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 .