Quintessence in a quandary: prior dependence in dark energy models
  The archetypal theory of dark energy is quintessence: a minimally coupled
scalar field with a canonical kinetic energy and potential. By studying random
potentials we show that quintessence imposes a restricted set of priors on the
equation of state of dark energy. Focusing on the commonly-used
parametrisation, $w(a)\approx w_0+w_a(1-a)$, we show that there is a natural
scale and direction in the $(w_0, w_a)$ plane that distinguishes quintessence
as a general framework. We calculate the expected information gain for a given
survey and show that, because of the non-trivial prior information, it is a
function of more than just the figure of merit. This allows us to make a
quantitative case for novel survey strategies. We show that the scale of the
prior sets target observational requirements for gaining significant
information. This corresponds to a figure of merit FOM$\gtrsim 200$, a
requirement that future galaxy redshift surveys will meet.
