A one-parameter formula for testing slow-roll dark energy: observational
  prospects
  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. Up
until now two-parameter descriptions of $w$ have been available, but this work
finds an additional approximation that leads to a single-parameter model. Using
it, we conduct a $\chi^2$ 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 $\Omega_m$ 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.
