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 parametrization, w(a) approximate to 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 nontrivial 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 greater than or similar to 200, a requirement that future galaxy redshift surveys will meet.