Asymptotic Accelerated Expansion in String Theory and the Swampland

TL;DR

This paper investigates whether string theory scalar potentials can produce accelerated cosmological expansion near infinite field limits, identifying potential loopholes and analyzing concrete F-theory examples to assess the conditions for such expansion.

Contribution

It introduces a new perspective on the conditions for asymptotic accelerated expansion in string theory, including a reformulation as a convex hull de Sitter conjecture.

Findings

Potential candidates for asymptotic accelerated expansion identified.

Loopholes to existing bounds on accelerated expansion found.

A convex hull de Sitter conjecture proposed for multi-moduli setups.

Abstract

We study whether the universal runaway behaviour of stringy scalar potentials towards infinite field distance limits can produce an accelerated expanding cosmology \`{a} la quintessence. We identify a loophole to some proposed bounds that forbid such asymptotic (at parametric control) accelerated expansion in 4d $\mathcal{N}=1$ supergravities, by considering several terms of the potential competing asymptotically. We then analyse concrete string theory examples coming from F-theory flux compactifications on Calabi-Yau fourfolds, extending previous results by going beyond weak string coupling to different infinite distance limits in the complex structure moduli space. We find some potential candidates to yield asymptotic accelerated expansion with a flux potential satisfying $\gamma=\frac{\|\nabla V\|}{V}<\sqrt{2}$ along its gradient flow. However, whether this truly describes an accelerated expanding cosmology remains as an open question until full moduli stabilization including the Kahler moduli is studied. Finally, we also reformulate the condition for forbidding asymptotic accelerated expansion as a convex hull de Sitter conjecture which resembles a convex hull scalar WGC for the membranes generating the flux potential. This provides a pictorial way to quickly determine the asymptotic gradient flow trajectory in multi-moduli setups and the value of $\gamma$ along it.