Dark Energy in String Theory

TL;DR

This paper explores string theory motivated models for Dark Energy, analyzing supergravity potentials and conditions for quintessence, and reviews thermal dark energy scenarios consistent with swampland conjectures.

Contribution

It identifies specific string-inspired scalar potentials that can support slow-roll quintessence and discusses thermal dark energy models aligned with swampland constraints.

Findings

Certain moduli potentials can support positive energy and slow-roll conditions.

Supergravity restrictions exclude some common quintessence models.

Thermal dark energy with hidden sectors can produce $w=-1$ and align with swampland conjectures.

Abstract

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 K\"ahler potentials for bulk and local moduli, and leading superpotentials of the form $W = W_0 + A e^{-a \Phi}$ or $W = W_0 + A \Phi^p$. Conditions on the scalar potential imposed by supergravity are very restrictive, ruling out e.g. quintessence with $K=-n\ln(\Phi+\bar{\Phi})$ and $W = W_0+A \Phi^p$. Out of the examples considered, one can simultaneously satisfy $V>0$ and $\epsilon_V<1$ only for a deformation-like modulus with $K = k_0 + \frac{|\Phi|^{2n}}{k1}$ and a blow-up like modulus with $K=k_0 +\frac{(\Phi+\bar{\Phi})^{2n}}{k_1}$ 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.