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How far can we push the SN measurements? Finding more and more SNe allows us to beat down statistical errors to arbitrarily small levels but, ultimately, systematic effects will limit the precision to which SNIa magnitudes can be applied to measure distances. Our best estimate is that it will be possible to control systematic effects from ground-based experiments to a level of ~ 0.03 mag. Carefully controlled ground-based experiments on 200 SNe will reach this statistical uncertainty in z = 0.1 redshift bins in the range z = 0.3 - 0.7, and is achievable within five years. A comparable quality low redshift sample, with 300 SNe in z = 0.02 - 0.08, will also be achievable in that time frame [2].

The SuperNova/Acceleration Probe (SNAP) collaboration (1) has proposed to launch a dedicated cosmology satellite [1, 68] - the ultimate SNIa experiment. This satellite will, if funded, scan many square degrees of sky, discovering well over a thousand SNIa per year and obtain their spectra and light curves out to z = 1.7. Besides the large numbers of objects and their extended redshift range, space-based observations will also provide the opportunity to control many systematic effects better than from the ground [21, 53]. Fig. 7 shows the expected precision in the SNAP and ground-based experiments for measuring w, assuming a flat Universe. Perhaps the most important advance will be the first studies of the time variation of the equation of state w (see the right panel of Fig. 7 and [40, 103]).

Figure 7

Figure 7. Future expected constraints on dark energy: Left panel: Estimated 68% confidence regions for a constant equation of state parameter for the dark energy, w, versus mass density, for a ground-based study with 200 SNe between z = 0.3 - 0.7 (open contours), and for the satellite-based SNAP experiment with 2,000 SNe between z = 0.3 - 1.7 (filled contours). Both experiments are assumed to also use 300 SNe between z = 0.02 - 0.08. A flat cosmology is assumed (based on Cosmic Microwave Background (CMB) constraints) and the inner (solid line) contours for each experiment include tight constraints (from large scale structure surveys) on OmegaM, at the ± 0.03 level. For the SNAP experiment, systematic uncertainty is taken as dm = 0.02(z / 1.7), and for the ground-based experiment, dm = 0.03(z / 0.5). Such ground-based studies will test the hypothesis that the dark energy is in the form of a cosmological constant, for which w = - 1 at all times. Middle panel: The same confidence regions for the same experiments not assuming the equation of state parameter, w, to be constant, but instead marginalizing over w', where w(z) = w0 + w'z. (Weller and Albrecht [103] recommend this parameterization of w(z) over the others that have been proposed to characterize well the current range of dark energy models.) Note that these planned ground-based studies will yield impressive constraints on the value of w today, w0, even without assuming constant w. In fact, these constraints are comparable to the current measurements of w assuming it is constant (shown in the right panel of Fig. 6). Right panel: Estimated 68% confidence regions of the first derivative of the equation of state, w', versus its value today, w0, for the same experiments.

With rapidly improving CMB data from interferometers, the satellites Microwave Anisotropy Probe (MAP) and Planck, and balloon-based instrumentation planned for the next several years, CMB measurements promise dramatic improvements in precision on many of the cosmological parameters. However, the CMB measurements are relatively insensitive to the dark energy and the epoch of cosmic acceleration. SNIa are currently the only way to directly study this acceleration epoch with sufficient precision (and control on systematic uncertainties) that we can investigate the properties of the dark energy, and any time dependence in these properties. This ambitious goal will require complementary and supporting measurements of, for example, OmegaM from CMB, weak lensing, and large scale structure. The SN measurements will also provide a test of the cosmological results independent from these other techniques, which have their own systematic errors. Moving forward simultaneously on these experimental fronts offers the plausible and exciting possibility of achieving a comprehensive measurement of the fundamental properties of our Universe.

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