Probing the evolution of the dark energy density with future supernova surveys

The time dependence of the dark energy density can be an important clue to the nature of dark energy in the universe. We show that future supernova data from dedicated telescopes (such as SNAP), when combined with data of nearby supernovae, can be used to determine how the dark energy density ρ_X(z) depends on redshift, if ρ_X(z) is not too close to a constant. For quantitative comparison, we have done an extensive study of a number of dark energy models. Based on these models we have simulated data sets in order to show that we can indeed reconstruct the correct sign of the time dependence of the dark energy density, outside of a degeneracy region centred on 1+w_0 \simeq-w_1 z_{\max }/3 (where z_max is the maximum redshift of the survey; for example, z_max = 1.7 for SNAP).