Dynamical de Sitter conjecture and quintessence model

TL;DR

This work extends the de Sitter swampland conjecture by incorporating the dynamical evolution of scalar fields, deriving a dynamical bound $-\frac{\partial_\tau V}{V} \ge 2\sqrt{\frac{D-2}{(D-d)(d-2)}} - \alpha \frac{\dot{\tau}^2}{V}$ that reduces to the conventional limit when the scalar velocity is small. By applying this to a quintessence model with an exponential potential $V=V_0 e^{-\lambda \tau}$ and solving the $d$-dimensional equations exactly, the authors map the allowed region for the slope parameter $\lambda$ as a function of the total dimension $D$, showing that kinetic terms can broaden the viable parameter space, especially in lower dimensions. The results suggest that dynamical contributions can reconcile quintessence with cosmological observations under quantum-gravity constraints, though they rely on specific higher-dimensional assumptions and neglect certain sectors (e.g., Higgs-like potentials) that may reintroduce tensions. Overall, the paper provides a rigorous framework for incorporating scalar-field dynamics into swampland criteria with potential implications for string compactifications and early/universe cosmology.

Abstract

The de Sitter conjecture yields a severe bound on possible vacua for a consistent quantum gravity. We extend the de Sitter conjecture by taking into account dynamics of the scalar field. We then apply such an extended de Sitter conjecture to a quintessence model of inflation for which dynamics of the scalar field is essential, and obtain an allowed region of parameters of the scalar potential wider than previously considered cases with the conventional de Sitter conjecture. The new bounds in the swampland conjecture could have implications in several situations to construct compactification models.

Figures (1)

• Figure 1: The allowed region of the parameter $\lambda$ for $d=4$ satisfying $f(\lambda)\le 0$ is depicted in the case of $D=11$ (a), $D=10$ (b), and $D=5$ (c). One can recognize that the lower bound of $\lambda$ increases as the number of total dimension $D$ decreases.