Testing the Swampland: $H_0$ tension

TL;DR

The paper tests whether Quintessence models constrained by the de Sitter Swampland bound can alleviate the H0 tension. By solving an H(z) evolution equation driven by a constant-λ Quintessence trajectory and fitting to low-z H(z) data with Planck or Riess priors, it shows that larger λ lowers the inferred H0, increasing the tension with local Riess measurements (tension rising from ~4.3σ to ~4.7σ under Planck priors). The ΛCDM limit (λ=0) remains closer to Planck's H0, while higher λ worsens agreement with Riess, regardless of prior. The results imply that simple Quintessence within the Swampland bound does not resolve the H0 discrepancy and highlight H0 tension as a robust litmus test for Swampland-consistent dark energy, motivating exploration of non-de Sitter cosmologies compatible with the bound.

Abstract

The de Sitter Swampland conjecture compels us to consider dark energy models where $λ(φ) \equiv |\nabla_φ V|/V$ is bounded below by a positive constant. Moreover, it has been argued for Quintessence models that the constant $λ$ scenario is the least constrained. Here we demonstrate that increasing $λ$ only exacerbates existing tension in the Hubble constant $H_0$. The identification of dark energy models that both evade observational bounds and alleviate $H_0$ tension constitutes a robust test for the Swampland program.

Figures (4)

• Figure 1: Integrating equation (\ref{['eq3']}) subject to the nominal boundary condition $H_0 = 70 \textrm{ km s}^{-1} \textrm{ Mpc}^{-1}$ leads to an increasing slope with increasing $\lambda$.
• Figure 2: Here we illustrate the consistency between the analytic and numerical solution ($\lambda = 0)$ with a Planck prior. This provides a consistency check on the numerical integration.
• Figure 3: We illustrate the best-fit values of $H_0$ as $\lambda$ is varied subject to a Planck prior for $H_0$. As is evident from the plot, larger values of $\lambda$ lead to lower values of $H_0$. We include the current Riess et al. value $H_0 = 74.03 \pm 1.42 \textrm{ km s}^{-1} \textrm{ Mpc}^{-1}$Riess:2019cxk for comparison.
• Figure 4: We illustrate the best-fit values of $H_0$ as $\lambda$ is varied subject to a Riess et al. prior for $H_0$. As is evident from the plot, larger values of $\lambda$ lead to lower values of $H_0$. We include the current Riess et al. value $H_0 = 74.03 \pm 1.42 \textrm{ km s}^{-1} \textrm{ Mpc}^{-1}$Riess:2019cxk for comparison.