Dark Energy in the Swampland

TL;DR

This paper examines how string Swampland criteria constrain dark energy models, analyzing current and future observational capabilities to distinguish between a cosmological constant and evolving scalar field models within these theoretical limits.

Contribution

It assesses the impact of string Swampland criteria on dark energy models and evaluates the observational precision needed to test these constraints.

Findings

Current constraints are compatible with Swampland criteria.

Future surveys will challenge quintessence models, pushing parameters below critical thresholds.

Decisive tests require unrealistically precise future observations.

Abstract

In this Letter, we study the implications of string Swampland criteria for dark energy in view of ongoing and future cosmological observations. If string theory should be the ultimate quantum gravity theory, there is evidence that exact de Sitter solutions with a positive cosmological constant cannot describe the fate of the late-time universe. Even though cosmological models with dark energy given by a scalar field $\pi$ evolving in time are not in direct tension with string theory, they have to satisfy the Swampland criteria $|\Delta\pi|<d\sim\mathcal{O}(1)$ and $|V'|/V>c\sim\mathcal{O}(1)$, where $V$ is the scalar field potential. In view of the restrictive implications that the Swampland criteria have on dark energy, we investigate the accuracy needed for future observations to tightly constrain standard dark-energy models. We find that current 3-$\sigma$ constraints with $c \lesssim 1.35$ are still well in agreement with the string Swampland criteria. However, Stage-4 surveys such as Euclid, LSST and DESI, tightly constraining the equation of state $w(z)$, will start putting surviving quintessence models into tensions with the string Swampland criteria by demanding $c<0.4$. We further investigate whether any idealised futuristic survey will ever be able to give a decisive answer to the question whether the cosmological constant would be preferred over a time-evolving dark-energy model within the Swampland criteria. Hypothetical surveys with a reduction in the uncertainties by a factor of $\sim20$ compared to Euclid would be necessary to reveal strong tension between quintessence models obeying the string Swampland criteria and observations by pushing the allowed values down to $c<0.1$. In view of such perspectives, there will be fundamental observational limitations with future surveys.