Quintessence and the Swampland: The Numerically Controlled Regime of Moduli Space

We provide a detailed discussion of the main theoretical and phenomenological challenges of quintessence model building in any numerically controlled regime of the moduli space of string theory. We argue that a working quintessence model requires a leading order non-supersymmetric (near) Minkowski vacuum with an axionic flat direction. This axion, when lifted by subdominant non-perturbative effects, could drive hilltop quintessence only for highly tuned initial conditions and a very low inflationary scale. Our analysis has two important implications. Firstly, scenarios which are in agreement with the swampland conjectures, such as those that include runaways, or supersymmetric AdS and Minkowski vacua, cannot give rise to phenomenologically viable quintessence with full computational control. This raises doubts on the validity of the swampland dS conjecture since it would imply a strong tension between quantum gravity and observations. Secondly, if data should prefer dynamical dark energy, axion models based on alignment mechanisms look more promising than highly contrived hilltop scenarios.