Casimir-Induced Quintessence in Dark Dimension

Abstract: We investigate a concrete realization of the Dark Dimension scenario, where a single large extra dimension is set at sub-millimeter scales. In this framework, the Casimir energy of bulk fields accounts for the observed dark energy. Working in a 5-dimensional setup with the Standard Model confined to a 4-dimensional brane, we derive the effective action for the radion. We demonstrate that a minimal model comprising only gravity and three right-handed bulk neutrinos typically yields a negative radion potential. To realize a positive vacuum energy, we consider some extensions with additional bulk degrees of freedom. These extensions generate a sufficiently flat positive potential that allows the radion to behave as a quintessence field, evolving slowly at the sub-eV scale. Finally, we analyze the evolution of the dark-energy equation-of-state parameter and show that our model is consistent with recent DESI BAO measurements, including the distance ratios $D_H/r_d$ and $D_M/r_d$.