Figures of merit for present and future dark energy probes
  We compare current and forecasted constraints on dynamical dark energy models
from Type Ia supernovae and the cosmic microwave background using figures of
merit based on the volume of the allowed dark energy parameter space. For a
two-parameter dark energy equation of state that varies linearly with the scale
factor, and assuming a flat universe, the area of the error ellipse can be
reduced by a factor of ~10 relative to current constraints by future
space-based supernova data and CMB measurements from the Planck satellite. If
the dark energy equation of state is described by a more general basis of
principal components, the expected improvement in volume-based figures of merit
is much greater. While the forecasted precision for any single parameter is
only a factor of 2-5 smaller than current uncertainties, the constraints on
dark energy models bounded by -1<w<1 improve for approximately 6 independent
dark energy parameters resulting in a reduction of the total allowed volume of
principal component parameter space by a factor of ~100. Typical quintessence
models can be adequately described by just 2-3 of these parameters even given
the precision of future data, leading to a more modest but still significant
improvement. In addition to advances in supernova and CMB data, percent-level
measurement of absolute distance and/or the expansion rate is required to
ensure that dark energy constraints remain robust to variations in spatial
curvature.
