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 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.

Figure 1

The error ${\sigma }_i$ for the five best determined modes for the fiducial parametrization (11) in the baseline scenario.

Figure 2

The error ${\sigma }_i$ for the five best determined modes for the fiducial parametrization (11) in the ideal scenario.

Figure 3

The error ${\sigma }_i$ for the five best determined modes for the fiducial parametrization (11) in the control scenario.

Figure 4

The four best determined eigenmodes for parametrization (11) using only supernovae. Solid line, dashed line, dash-dotted line, and dotted line correspond to first, second, third, and fourth modes, respectively.

Figure 5

The four best determined eigenmodes using parametrization (11) for the baseline scenario. Solid line, dashed line, dash-dotted line, and dotted line correspond to first, second, third, and fourth modes, respectively.

Figure 6

The four best determined eigenmodes using parametrization (11) for the ideal scenario. Solid line, dashed line, dash-dotted line, and dotted line correspond to first, second, third, and fourth modes, respectively.

Figure 7

The four best determined eigenmodes using parametrization (11) for the control scenario. Solid line, dashed line, dash-dotted line, and dotted line correspond to first, second, third, and fourth modes, respectively.

Figure 8

Reconstruction of the equation of state parameter (11) using only supernovae with the minimization of the risk method.

Figure 9

Reconstruction of the equation of state parameter (11) in the baseline scenario with the minimization of the risk method.

Figure 10

Reconstruction of the equation of state parameter (11) in the baseline scenario with the normalization of the error on the modes method.