Testing the Swampland: $H_0$ tension

The de Sitter Swampland conjecture compels us to consider dark energy models where $\lambda(\phi) \equiv |\nabla_{\phi} V|/V$ is bounded below by a positive constant. Moreover, it has been argued for Quintessence models that the constant $\lambda$ scenario is the least constrained. Here we demonstrate that increasing $\lambda$ 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.