Measuring Time Dependence of Dark Energy Density from Type Ia Supernova Data

Observations of high redshift supernovae imply an accelerating Universe whichcan only be explained by an unusual energy component such as vacuum energy orquintessence. To assess the ability of current and future supernova data toconstrain the properties of the dark energy, we allow its density to havearbitrary time-dependence, $\rho_X(z)$. This leads to an equation of state forthe dark energy, $w_X(z)=p_X(z)/\rho_X(z)$, which is a free function ofredshift $z$. We find that current type Ia supernova (SNe Ia) data areconsistent with a cosmological constant, with large uncertainties at $z\ga0.5$. We show that $\rho_X(z)/\rho_X(z=0)$ can be measured reasonably well toabout $z=1.5$ using type Ia supernova data from realistic future SN Ia pencilbeam surveys, provided that the weak energy condition (energy density of matteris nonnegative for any observer) is imposed. While it is only possible to differentiate between different models (say,quintessence and k-essence) at $z \la 1.5$ using realistic data, the correcttrend in the time-dependence of the dark energy density can be clearly detectedout to $z=2$, even in the presence of plausible systematic effects. This wouldallow us to determine whether the dark energy is a cosmological constant, orsome exotic form of energy with a time-dependent density.Comment: final version to appear in ApJ, 552, May 10 (2001