Dark Energy in the Swampland

TL;DR

This work probes whether string-theory Swampland criteria constrain late-time dark energy modeled as a quintessence field with potential $V(\pi)$. By mapping the Swampland conditions $|\Delta\pi|<d$ and $|V'/V|>c$ to the dynamical parameter $\lambda=-M_P V'/V$ and the CPL-based equation of state $w(z)$, the authors translate theoretical bounds into observational limits on $w_0$ and $w_a$ and hence on $c$/$\lambda$. Using current data, they find $\lambda\lesssim 0.9$ (2$\sigma$) and $\lambda\lesssim 1.35$ (3$\sigma$), compatible with the Swampland but leaving many quintessence models viable. Stage-4 surveys are forecast to tighten to $\lambda\lesssim 0.4$, potentially putting surviving quintessence models in tension with the swampland conjectures; reaching $\lambda\lesssim 0.1$ would require unrealistically large improvements, indicating fundamental observational limits in distinguishing a cosmological constant from evolving dark energy within this framework.

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 $π$ evolving in time are not in direct tension with string theory, they have to satisfy the Swampland criteria $|Δπ|<d\sim\mathcal{O}(1)$ 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-$σ$ 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.

Figures (3)

• Figure 1: The figure shows 1- and 2-$\sigma$ upper bounds on the reconstructed equation of state $w(z)$ as a function of redshift, according to the analysis described in the text. We use the constraints obtained from SNeIa, CMB, BAO and $H_0$ measurements shown in Fig. 21 of Scolnic:2017caz (the yellow contours there) combined with the CPL parameterization of $w(z)$. We find that our 1-$\sigma$ bound reproduces the tight constraint addressed as a 3-$\sigma$ upper bound in Agrawal:2018own. We also extrapolate the uncertainty in order to plot the 3-$\sigma$ upper bound. The dotted lines show the equation of state as a function of redshift for different quintessence models with different $\lambda$ values for comparison.
• Figure 2: Similar to Fig. \ref{['fig_wDEvsz']}, upper bounds on $w(z)$ are shown here as expected from the target uncertainties in $w_0$ and $w_a$ given in Tab. 2.2 of the Euclid Red Book. At the 3-$\sigma$ level, $\lambda$ will be constrained to $\lambda\lesssim0.4$.
• Figure 3: Upper bounds on $w(z)$ to be expected from a hypothetical future survey with uncertainties on $w_0$ and $w_a$ lowered by 50% compared to the values given in the Euclid Red Book. At the 3-$\sigma$ level, only $\lambda\lesssim0.3$ will be allowed, which would get into tension with the Swampland criteria. Constraining $\lambda$ down to $\lambda\lesssim0.1$ is only achievable if the uncertainties could be reduced by a factor of $\sim20$ compared to Euclid.