Quintessence in a quandary: prior dependence in dark energy models

TL;DR

This paper investigates how quintessence dark energy models impose specific priors on the equation of state parameters, influencing survey strategies and the expected information gain from future observations.

Contribution

It characterizes the prior constraints of quintessence models on dark energy parameters and assesses their impact on survey design and information gain calculations.

Findings

Quintessence models restrict the (w0, wa) parameter space.

A natural scale in the (w0, wa) plane distinguishes quintessence.

Future galaxy surveys will meet the FOM > 200 requirement.

Abstract

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.