Cosmic Acceleration and Turns in the Swampland

TL;DR

This paper argues that in string theory, field trajectories leading to cosmic acceleration with rapid turns are incompatible with the Swampland Distance Conjecture, implying constraints on multi-field models and a tension with de Sitter expansion.

Contribution

It demonstrates that rapid turns in field trajectories near the boundary of moduli space are in the Swampland, constraining multi-field inflationary models in string theory.

Findings

Turning rate is bounded by the Hubble rate and acceleration parameter.

Field trajectories near the boundary are nearly geodesic.

Implications for the viability of multi-field inflation models.

Abstract

We argue that field trajectories, which lead to cosmic acceleration and feature rapid turns near the boundary of the moduli space, are in the Swampland. We obtain this result by assuming the validity of the Swampland Distance Conjecture (SDC) in the presence of a positive scalar potential and by focusing on hyperbolic spaces, as prototype geometries of infinite distance limits of Calabi-Yau compactifications. We find that, in a quasi-de Sitter space with Hubble rate $H$ and acceleration parameter $\epsilon$, the turning rate $\Omega$ is upper bounded such as $\Omega/H<\mathcal{O}(\sqrt{\epsilon})$. Therefore, field trajectories consistent with the SDC can only have a negligible deviation from geodesics. This has direct implications for the realization and consistency of multi-field scenarios in string theory. Moreover, it implies a tension between asymptotic accelerating expansion, consistent with observations, and the de Sitter conjecture.