Will Upcoming Observations Distinguish Between Slow-Roll Dark Energy and a Cosmological Constant?

Numerous upcoming observations, such as WFIRST, BOSS, BigBOSS, LSST, Euclid, and Planck, will constrain dark energy (DE)'s equation of state with great precision. They may well find the ratio of pressure to energy density, w, is -1, meaning DE is equivalent to a cosmological constant. However, many time-varying DE models have also been proposed. A single parametrization to test a broad class of them and that is itself motivated by a physical picture is therefore desirable. We suggest the simplest model of DE has the same mechanism as inflation, likely a scalar field slowly rolling down its potential. If this is so, DE will have a generic equation of state and the Universe will have a generic dependence of the Hubble constant on redshift independent of the potential's starting value and shape. This equation of state and expression for the Hubble constant offer the desired model-independent but physically motivated parametrization, because they will hold for most of the standard scalar-field models of DE such as quintessence and phantom DE. Using it, we conduct a χ^2 analysis and find that experiments in the next seven years should be able to distinguish any of these time-varying DE models on the one hand from a cosmological constant on the other to 73% confidence if w today differs from -1 by 3.5%. In the limit of perfectly accurate measurements of Ω_m and H_0, this confidence would rise to 96%. We also include discussion of the current status of DE experiment, a table compiling the techniques each will use, and tables of the precisions of the experiments for which this information was available at the time of publication.