Consistency of local and astrophysical tests of the stability of
  fundamental constants
  Tests of the stability of nature's fundamental constants are one of the
cornerstones of the ongoing search for the new physics which is required to
explain the recent acceleration of the universe. The two main settings for
these tests are high-resolution spectroscopy of astrophysical systems (mainly
in low-density absorption clouds along the line of sight of bright quasars) and
laboratory comparisons of pairs of atomic clocks. Here we use standard
chi-square techniques to perform a global analysis of all currently available
data, studying both the consistency of tests of stability of different
constants (specifically the fine-structure constant $\alpha$, the
proton-to-electron mass ratio $\mu$ and the proton gyromagnetic ratio $g_p$)
and the consistency between local laboratory and astrophysical tests. We start
by doing a model-independent analysis (studying the internal consistency of the
various available datasets) but also explore specific phenomenological models
motivated by string theory and grand unification. Overall there is weak (one to
two sigma) evidence of variations, at the level of up to a few parts per
million, 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 astrophysical
facilities, such as the ESPRESSO spectrograph, should be able to confirm or
rule out these hints.
