Importance of supernovae at $z>\mathrm{}1.5\mathrm{}$ to probe dark energy

The accelerating expansion of the universe suggests that an unknown component with strongly negative pressure, called dark energy, currently dominates the dynamics of the universe. Such a component makes up $\sim 70\%$ of the energy density of the universe yet has not been predicted by the standard model of particle physics. The best method for exploring the nature of this dark energy is to map the recent expansion history, at which type Ia supernovae have proved adept. We examine here the depth of survey necessary to provide a precise and qualitatively complete description of dark energy. A realistic analysis of parameter degeneracies, allowance for natural time variation of the dark energy equation of state, and systematic errors in astrophysical observations all demonstrate the importance of a survey covering the full range $0<z\lesssim 2$ for revealing the nature of dark energy.