Figures of merit for present and future dark energy probes

TL;DR

This paper evaluates how future supernova and CMB data will significantly improve constraints on dark energy models, especially when using principal component analysis, reducing the allowed parameter space by up to two orders of magnitude.

Contribution

It introduces a volume-based figure of merit for dark energy constraints and demonstrates substantial improvements with future data, especially for models with multiple parameters.

Findings

Future data can reduce the dark energy parameter space volume by a factor of ~100.

Constraints on a two-parameter dark energy model improve by a factor of 10.

Principal component analysis reveals that 2-3 parameters suffice to describe typical quintessence models.

Abstract

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.