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.

S-Dual Quintessence and Its Cosmological Implications

The paper under discussion advances a novel model of dark energy that integrates quintessence fields with an $S$-dual potential. It critically examines the consistency of this model with prevailing Swampland conjectures and the empirical data from the recent DESI DR2 results. The $S$-dual quintessence model represents a minimalistic approach to addressing cosmic acceleration, featuring a potential of the form ( V(\phi) = \Lambda \ \text{sech} (\sqrt{2} \, \phi/M_p) ).

Core Concepts and Theory

The concept of $S$-duality, essential in both gauge theories and string theory, involves transformation properties linking strong and weak couplings. In this framework, the quintessence model proposes that the field (\phi) is governed by a potential symmetric under $S$-duality. This symmetry enforces a specific potential form that is simple yet consistent with conjectures from the Swampland program. The Swampland conjectures, namely the distance conjecture, de Sitter (dS) conjecture, and trans-Planckian censorship conjecture (TCC), limit effective field theories that could be compatible with quantum gravity.

Confrontation with Swampland Conjectures

The authors assert that the $S$-dual potential aligns well with the distance conjecture, which restricts field variations over trans-Planckian distances to prevent destabilization through the emergence of light states. Furthermore, the model satisfies the refined dS conjecture by maintaining specific bounds on the potential's gradient and curvature. The TCC condition requiring certain growth rates of cosmological perturbations is met, rendering the model plausible within this theoretical scope.

Comparison with DESI DR2 Observations

One of the paper's significant contributions is juxtaposing the $S$-dual quintessence model against the axion-like potential explored in DESI DR2 data sets. The DESI DR2 findings suggest an evolving dark energy, potentially challenging the traditional $\Lambda$CDM paradigm. The axion-like potential ( V(\phi) = m_a^2 \ f_a^2 \ [ 1 + \cos(\phi/f_a)] ), fits empirical data under conditions where dark energy evolves with redshift. This empirical evidence indicates compatibility with an $S$-dual potential form, particularly the nearly indistinguishable shape and behavior under cosmological surveys.

Implications and Future Directions

The results from this paper indicate that $S$-dual quintessence can be a compelling candidate for explaining cosmic acceleration while remaining consistent with theoretical Swampland constraints. It offers a streamlined model with fewer parameters than traditional axion-like approaches, enhancing predictability and viability for future testing against cosmological observations.

Conclusion

The examination of $S$-dual quintessence presents robust theoretical grounding and empirical support in light of astrophysical data. By advocating a minimalistic but well-constrained viewpoint on dark energy, this research enriches the discourse on cosmological models aligning fundamental physics with observational cosmology, thus paving the way for anticipated refinements in our understanding of late universe dynamics. Future advancements in observational cosmology will variably test these models, providing either greater empirical support or necessitating further theoretical refinement.