Supernovae and the nature of the dark energy

The use of Type Ia supernovae as calibrated standard candles is one of the most powerful tools to study the expansion history of the universe and thereby its energy components. While the analysis of some 50 supernovae at redshifts around z 0:5 has provided strong evidence for an energy component with negative pressure, \dark energy", more data is needed to enable an accurate estimate of the amount and nature of this energy. This might be accomplished by a dedicated space telescope, the SuperNova / Acceleration Probe (2000; SNAP), which aims at collecting a large number of supernovae with z< 2. In this paper we assess the ability of the SNAP mission to determine various properties of the \dark energy." To exemplify, we expect SNAP, if operated for three years to study Type Ia supernovae, to be able to determine the parameters in a linear equation of state w(z )= w0 +w1z to within a statistical uncertainty of0:04 for w0 and +0:15 0:17 for w1 assuming that the universe is known to be flat and an independent high precision (m =0 :015) measurement of the mass density m, is used to constrain the t. A further improvement can be obtained if, in addition to the high-z events, a large number of low-z supernovae are included in the sample.