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Tests of the stability of nature's fundamental constants are one of thecornerstones of the ongoing search for the new physics which is required toexplain the recent acceleration of the universe. The two main settings forthese tests are high-resolution spectroscopy of astrophysical systems (mainlyin low-density absorption clouds along the line of sight of bright quasars) andlaboratory comparisons of pairs of atomic clocks. Here we use standardchi-square techniques to perform a global analysis of all currently availabledata, studying both the consistency of tests of stability of differentconstants (specifically the fine-structure constant $\alpha$, theproton-to-electron mass ratio $\mu$ and the proton gyromagnetic ratio $g_p$)and the consistency between local laboratory and astrophysical tests. We startby doing a model-independent analysis (studying the internal consistency of thevarious available datasets) but also explore specific phenomenological modelsmotivated by string theory and grand unification. Overall there is weak (one totwo sigma) evidence of variations, at the level of up to a few parts permillion, and reasonable agreement between laboratory and astrophysical tests.This result holds even if one removes from the analysis the Webb {\it et al.}archival dataset of $\alpha$ measurements. Forthcoming astrophysicalfacilities, such as the ESPRESSO spectrograph, should be able to confirm orrule out these hints.

Consistency of local and astrophysical tests of the stability of fundamental constants