Variation of fundamental parameters and dark energy. A principal
  component approach
  We discuss methods based on Principal Component Analysis to constrain the
dark energy equation of state using a combination of Type Ia supernovae at low
redshift and spectroscopic measurements of varying fundamental couplings at
higher redshifts. We discuss the performance of this method when future
better-quality datasets are available, focusing on two forthcoming ESO
spectrographs - ESPRESSO for the VLT and CODEX for the E-ELT - which include
these measurements as a key part of their science cases. These can realize the
prospect of a detailed characterization of dark energy properties almost all
the way up to redshift 4.
