Abstract
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 data sets are available, focusing on two forthcoming European southern observatory (ESO) spectrographs---Echelle spectrograph for rocky exoplanet and stable spectroscopic observations (ESPRESSO) for the very large telescope (VLT) and Cosmic dynamics explorer (CODEX) for the European extremely large telescope (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.
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