Variation of fundamental parameters and dark energy. A principal component approach

We discuss methods based on Principal Component Analysis for reconstructing the dark energy equation of state and constraining its evolution, 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 all the way up to redshift 4. Cosmology has recently entered a precision, datadriven era. The availability of ever larger, higher-quality datasets has led to the so-called concordance model. This is a remarkably simple model (with a small number of free parameters) which provides a very good fit to the existing data. However, there is a price to pay for this success: the data suggests that 96% of the contents of the universe is in a still unknown form. This is often called the dark component of the universe. Whatever this may be, all the evidence suggests that it is not composed by the protons, neutrons and electrons that we are familiar with, but it must be in some form never seen in the laboratory. Current best estimates suggest that this dark component is in fact a combination of two distinct components. The first is called dark matter (making about 23% of the universe) and it is clustered in large-scale structures like galaxies. The second, which has gravitational properties very similar to those of the cosmological constant first proposed by Einstein, is called dark energy and currently dominating the universe, with about 73% of the density of the universe Understanding what constitutes this dark energy is one of the most important problems of modern cosmology. In particular, we would like to find out if it is indeed a cosmological constant [1], since there are many possible alternatives [2]. These alternative models often involve scalar fields, an example of which is the Higgs field which the LHC is searching for. A further alternative are the