Recent variations of fundamental parameters and their implications for
  gravitation
  We compare the sensitivity of a recent bound on time variation of the fine
structure constant from optical clocks with bounds on time varying fundamental
constants from atomic clocks sensitive to the electron-to-proton mass ratio,
from radioactive decay rates in meteorites, and from the Oklo natural reactor.
Tests of the Weak Equivalence Principle also lead to comparable bounds on
present time variations of constants, as well as putting the strongest limits
on variations tracking the gravitational potential. For recent time variations,
the "winner in sensitivity" depends on possible relations between the
variations of different couplings in the standard model of particle physics.
WEP tests are currently the most sensitive within scenarios with unification of
gauge interactions. A detection of time variation in atomic clocks would favour
dynamical dark energy and put strong constraints on the dynamics of a
cosmological scalar field.
