Model-independent predictions for smooth cosmic acceleration scenarios

Through likelihood analyses of both current and future data that constrain both the expansion history of the Universe and the clustering of matter fluctuations, we provide falsifiable predictions for three broad classes of models that explain the accelerated expansions of the Universe: ΛCDM, the quintessence scenario, and a more general class of smooth dark energy models that can cross the phantom barrier w(z)=-1. Our predictions are model independent in the sense that we do not rely on a specific parametrization, but we instead use a principal component (PC) basis function constructed a priori from a noise model of supernovae and cosmic microwave background observations. For the supernovae measurements, we consider two type of surveys: the current JLA and the upcoming WFIRST surveys. We show that WFIRST will be able to improve growth predictions in curved models significantly. The remaining degeneracy between spatial curvature and w(z) could be overcome with improved measurements of σ8Ωm1/2, a combination that controls the amplitude of the growth of structure. We also point out that a PC-based figure of merit reveals that the usual two-parameter description of w(z) does not exhaust the information that can be extracted from current data (JLA) or future data (WFIRST).