Dark Energy in String Theory

We consider various candidates for Dark Energy, motivated by string theory. Several no-go theorems push de Sitter string vacua, with w=-1, to the limits of theoretical control, and all known examples depend on a delicate interplay between different string theoretic ingredients. On the other hand, runaway moduli directions are ubiquitous in string theory, and could plausibly source slow-roll quintessence. We consider various candidate supergravity potentials, motivated by string theory, including single-field Kaehler potentials for bulk and local moduli, and leading superpotentials of the form W = W₀ + A e^-a or W = W₀ + A ᵖ. Conditions on the scalar potential imposed by supergravity are very restrictive, ruling out e. g. quintessence with K=-n (+) and W = W₀+A ᵖ. Out of the examples considered, one can simultaneously satisfy V>0 and V<1 only for a deformation-like modulus with K = k₀ + ||^2nk1 and a blow-up like modulus with K=k₀ + (+) ^{2n}k₁ when the leading order in the perturbative superpotential, p, is equal to n. We also review the scenario of Thermal Dark Energy, where thermal effects in a light hidden sector hold a scalar field up away from the minimum of its zero-temperature potential. This provides a viable model of Dark Energy with w=-1, consistent with known swampland conjectures, and motivates further early Thermal Dark Energy epochs with potentially observable consequences.