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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.
Given a class of dark energy models, constraints from one set of cosmic acceleration observables make predictions for other observables. Here we present the allowed ranges for the expansion rate H(z), distances D(z), and the linear growth function G( z) (as well as other, derived growth observables) from the current combination of cosmological measurements of supernovae, the cosmic microwave background, baryon acoustic oscillations, and the Hubble constant. With a cosmological constant as the dark energy and assuming near-minimal neutrino masses, the growth function is already predicted to better than 2% precision at any redshift, with or without spatial curvature. Direct measurements of growth that match this precision offer the opportunity to stringently test and potentially rule out a cosmological constant. While predictions in the broader class of quintessence models are weaker, it is remarkable that they are typically within a factor of 2-3 of forecasts for future space-based supernovae and Planck CMB measurements. In particular, measurements of growth at any redshift, or the Hubble constant H_0, that exceed LambdaCDM predictions by substantially more than 2% would rule out not only a cosmological constant but also the whole quintessence class, with or without curvature and early dark energy. Barring additional systematic errors hiding in the data, such a discovery would require more exotic explanations of cosmic acceleration such as phantom dark energy, dark energy clustering, or modifications of gravity.
The angular power spectrum of the cosmic microwave background temperature anisotropy observed by WMAP has an anomalous dip at l~20 and bump at l~40. One explanation for this structure is the presence of features in the primordial curvature power spec trum, possibly caused by a step in the inflationary potential. The detection of these features is only marginally significant from temperature data alone. However, the inflationary feature hypothesis predicts a specific shape for the E-mode polarization power spectrum with a structure similar to that observed in temperature at l~20-40. Measurement of the CMB polarization on few-degree scales can therefore be used as a consistency check of the hypothesis. The Planck satellite has the statistical sensitivity to confirm or rule out the model that best fits the temperature features with 3 sigma significance, assuming all other parameters are known. With a cosmic variance limited experiment, this significance improves to 8 sigma. For tests of inflationary models that can explain both the dip and bump in temperature, the primary source of uncertainty is confusion with polarization features created by a complex reionization history, which at most reduces the significance to 2.5 sigma for Planck and 5-6 sigma for an ideal experiment. Smoothing of the polarization spectrum by a large tensor component only slightly reduces the ability of polarization to test for inflationary features, as does requiring that polarization is consistent with the observed temperature spectrum given the expected low level of TE correlation on few-degree scales. A future polarization satellite would enable a decisive test of the feature hypothesis and provide complementary information about the shape of a possible step in the inflationary potential. (Abridged.)
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