Probing dark energy: Methods and strategies

The presence of dark energy in the Universe is inferred directly from the accelerated expansion of the Universe, and, indirectly, from measurements of cosmic microwave background (CMB) anisotropy. Dark energy contributes about two-thirds of the critical density, is smoothly distributed, has large negative pressure, and is very mysterious. For now, all of its discernible cosmological consequences follow from its effect on the expansion rate of the Universe. Absent a compelling theoretical model (or even a class of models), we describe the dark energy by its equation of state ${w=p}_{X}/{\ensuremath{\rho}}_{X}$ which is allowed to vary with time. We describe and compare different approaches for determining $w(t),$ including a magnitude-redshift (Hubble) diagram, number counts of galaxies and clusters, and CMB anisotropy. We focus particular attention on the use of a sample of several thousand type Ia supernova with redshifts $z\ensuremath{\lesssim}1.7,$ as might be gathered by the proposed SNAP satellite. Among other things, we derive optimal strategies for constraining cosmological parameters using type Ia supernovae. The redshift range $z\ensuremath{\simeq}0.2\ensuremath{-}2$ has the most leverage for probing ${w}_{X};$ supernovae and number counts appear to have the most potential to probe dark energy. Because the expansion rate depends upon both $w(t)$ and ${\ensuremath{\Omega}}_{M},$ an independent measurement of the matter density is critical for obtaining the most information about dark energy from cosmological observations.