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 $D_M/r_d$.

Figures (4)

• Figure 1: The effective potential determined by the Casimir energy. The additional particle content in the 5-dimensional theory consists of two massive gauge bosons and two massless fermions. In this figure, we take $R_0 = 83\, \textrm{eV}^{-1}=16.4\,\mu\textrm{m}$, which corresponds to choosing $R_0 = \lambda \Lambda_{\rm c.c.}^{-1/4}$ with $\lambda \sim 10^{-1}$Montero:2022prj. The vertical axis represents $V(b) \,[\text{eV}^4]$.
• Figure 2: Equation-of-state parameter $w(z)$ for the Dark-Dimension model. The red dashed line and blue solid line represent $w_{\rm eff}(z)$ and $w_{\phi}(z)$ for $c=0.005$. The black solid line and gray area represent the constraints of $w(z)$ for CPL model using DESI+CMB+DESY5 DESI:2025zgx.
• Figure 3: This plot represents the BAO observable $D_H/r_d$. The black dashed and the red solid lines represent the $\Lambda$CDM ($\Omega_{\rm m,0}=0.3,~\Omega_{\Lambda}=0.7$) and the Dark-Dimension ($c=0.005$) model, respectively. Blue points and error bars are observational data from DESI DR2 summarized in Tab. \ref{['tab:DESIDR2_data']}. In this analysis, we used $r_d=147.1~{\rm Mpc}$.
• Figure 4: This plot represents the BAO observable $D_M/r_d$. The black dashed and the red solid line represent the $\Lambda$CDM ($\Omega_{\rm m,0}=0.3,~\Omega_{\Lambda}=0.7$) and the Dark-Dimension ($c=0.005$) model, respectively. Blue points and error bars are observational data from DESI DR2 summarized in Tab. \ref{['tab:DESIDR2_data']}. In this analysis, we used $r_d=147.1~{\rm Mpc}$.