We provide evidence that slow roll is not possible in any parametrically controlled regime of the moduli space of string theory. This is proven in full generality in the asymptotic limit of the moduli space of type II and heterotic Calabi-Yau compactifications for the dilaton and any number of Kähler moduli. Our results suggest that in order to build quintessence into string theory one must work in the interior of moduli space where numerical, even if not parametric, control could still be achieved.

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.

We propose a mechanism that generates a naturally light dark energy field (with Hubble scale mass), starting from a theory with exclusively high scale (Planckian) couplings. It is derived from the clockwork model, with O(100) scalar fields interacting among themselves as well as with a 4-form field strength. We explicitly embed our model in type IIA supergravity. We also give an alternative interpretation in a braneworld set-up.

We argue that, for string compactifications broadly consistent with swampland constraints, dark energy is likely to signal the beginning of the end of our universe as we know it, perhaps even through decompactification, with possible implications for the cosmological coincidence problem. Thanks to the scarcity (absence?) of stable de Sitter vacua, dark energy in string theory is assumed to take the form of a quintessence field in slow roll. As it rolls, a tower of heavy states will generically descend, triggering an apocalyptic phase transition in the low energy cosmological dynamics after at most a few hundred Hubble times. As a result, dark energy domination cannot continue indefinitely and there is at least a percentage chance that we find ourselves in the first Hubble epoch. We use a toy model of quintessence coupled to a tower of heavy states to explicitly demonstrate the breakdown in the cosmological dynamics as the tower becomes light. This occurs through a large number of corresponding particles being produced after a certain time, overwhelming quintessence. We also discuss some implications for early universe inflation.

In this paper we consider the Dvali and Gómez assumption that the end state of a gravitational collapse is a Bose-Einstein condensate of gravitons. We then construct the two Gross-Pitaevskii equations for a static and spherically symmetric configuration of the condensate. These two equations correspond to the constrained minimisation of the gravitational Hamiltonian with respect to the redshift and the Newtonian potential, per given number of gravitons. We find that the effective geometry of the condensate is the one of a gravastar (a DeSitter star) with a sub-Planckian cosmological constant, for masses larger than the Planck scale. Thus, a condensate corresponding to a semiclassical black hole, is always quantum and weakly coupled. Finally, we obtain that the boundary of our gravastar, although it is not the location of a horizon, corresponds to the Schwarzschild radius.