Dark energy: The observational challenge

Nearly all proposed tests for the nature of dark energy measure some combination of four fundamental observables: the Hubble parameter H(z), the distance-redshift relation d(z), the age-redshift relation t(z), or the linear growth factor D1(z). I discuss the sensitivity of these observables to the value and redshift history of the equation of state parameter w, emphasizing where these different observables are and are not complementary. Demonstrating time-variability of w is difficult in most cases because dark energy is dynamically insignificant at high redshift. Time-variability in which dark energy tracks the matter density at high redshift and changes to a cosmological constant at low redshift is relatively easy to detect. However, even a sharp transition of this sort at zc = 1 produces only percent-level differences in d(z) or D1(z) over the redshift range 0.4 ⩽ z ⩽ 1.8, relative to the closest constant-w model. Estimates of D1(z) or H(z) at higher redshift, potentially achievable with the Lyα forest, galaxy redshift surveys, and the CMB power spectrum, can add substantial leverage on such models, given precise distance constraints at z < 2. The most promising routes to obtaining sub-percent precision on dark energy observables are space-based studies of Type Ia supernovae, which measure d(z) directly, and of weak gravitational lensing, which is sensitive to d(z), D1(z), and H(z).