  Dynamical scalar fields in an effective four-dimensional field theory are
naturally expected to couple to the rest of the theory's degrees of freedom,
unless some new symmetry is postulated to suppress these couplings. In
particular, a coupling to the electromagnetic sector will lead to spacetime
variations of the fine-structure constant, $\alpha$. Astrophysical tests of the
space-time stability of $\alpha$ are therefore a powerful probe of new physics.
Here we use ESPRESSO and other contemporary measurements of $\alpha$, together
with background cosmology data, local laboratory atomic clock and Weak
Equivalence Principle measurements, to place stringent constraints on the
simplest examples of the two broad classes of varying $\alpha$ models:
Bekenstein models and quintessence-type dark energy models, both of which are
parametric extensions of the canonical $\Lambda$CDM model. In both cases,
previously reported constraints are improved by more than a factor of ten. This
improvement is largely due to the very strong local constraints, but
astrophysical measurements can help to break degeneracies between cosmology and
fundamental physics parameters.
