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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) w₀+w₀ (1-a), we show that there is a natural scale and direction in the (w₀, w₀) 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 FOM200, a requirement that future galaxy redshift surveys will meet.
Marsh et al. (Tue,) studied this question.