Reconstructing the evolution of dark energy with variations of
  fundamental parameters
  Under the assumption that the variations of parameters of nature and the
current acceleration of the universe are related and governed by the evolution
of a single scalar field, we show how information can be obtained on the nature
of dark energy from observational detection of (or constraints on) cosmological
variations of the fine structure constant and the proton-to-electron mass
ratio. We also comment on the current observational status, and on the
prospects for improvements with future spectrographs such as ESPRESSO and
CODEX.
