S-dual Quintessence, the Swampland, and the DESI DR2 Results

Abstract

We propose a dark energy model in which a quintessence field $\phi$ rolls near the vicinity of a local maximum of its potential characterized by the simplest $S$ self-dual form $V(\phi) = \Lambda \ {\rm sech}(\sqrt{2} \, \phi/M_p)$, where $M_p$ is the reduced Planck mass and $\Lambda \sim 10^{-120} M_p^4$ is the cosmological constant. We confront the model with Swampland ideas and show that the $S$-dual potential is consistent with the distance conjecture, the de Sitter conjecture, and the trans-Planckian censorship conjecture. We also examine the compatibility of this phenomenological model with the intriguing DESI DR2 results and show that the shape of the $S$-dual potential is almost indistinguishable from the axion-like potential, $V (\phi) = m_a^2 \ f_a^2 \ [ 1 + \cos(\phi/f_a)]$, with $m_a$ and $f_a$ parameters fitted by the DESI Collaboration to accommodate the DR2 data. The self-dual potential has the advantage that one starts at the self-dual point and this is a theoretical motivation, because as the universe cools off the $\mathbb{Z}_2$ symmetry gets broken leading to a natural rolling away from the symmetric point.