Casimir Energy Stabilization of Standard Model Landscape in Dark Dimension

TL;DR

The paper presents a concrete realization of a dark dimension by compactifying the 5D Standard Model plus gravity on an orbifold and stabilizing the radion with Casimir energy. The resulting 4D effective theory yields a de Sitter vacuum with a small positive cosmological constant and neutrino masses consistent with observations, while the radion remains ultra-light, prompting screening mechanisms for compatibility with gravity tests. It also discusses chirality realization via orbifolding and explores axio-chameleon scenarios as routes to realistic phenomenology. Overall, the work connects Casimir-stabilized extra dimensions to SM physics and cosmology, highlighting how neutrino data and vacuum energy considerations can fix the radion dynamics and the 4D cosmological constant, while identifying challenges and promising extensions for a fully realistic model.

Abstract

In this paper we present a realization of dark dimension. We consider the 5D standard model coupling to gravity with one dimension compactified on an orbifold, which is seen as dark dimension of size R. We stabilize the radion by casimir effect wrapping around compact dimension and recover the neutrino mass and 4D cosmological constant with the observed value. Orbifold can lead to a natural resolution of chirality problem in 5D at low energy, which we briefly discussed in the paper. Although we found that the radion mass is too light to survive under solar system tests of GR, several screening mechanisms might give us a solution, for example, Chameleon mechanism.

Figures (4)

• Figure 1: Effective potential for radion field in the case of three different value of $\Lambda_5$: a) $\Lambda_5=1\times 10^{-12}eV^5$ with an anti de-Sitter vacuum at $R=16.3$$eV^{-1}=3.2156\mu m$. b) $\Lambda_5=3\times 10^{-12}eV^5$, which produced a de-Sitter vacuum at $R=16.8$$eV^{-1}=3.3146\mu m$. c) $\Lambda_5=7\times 10^{-12}eV^5$ with runaway potential. In the plot we've fixed $r^2=107 eV^{-2}$ so that we can reproduce the correct value for $\Lambda_4$ in de-Sitter case at critical $R$: $\Lambda_4=V(R_c)\approx 3.3 \times 10^{-11} eV^4$.
• Figure 2: Contributions from different fields are shown. In the plot we took $\Lambda_5=3\times 10^{-12}eV^5$.
• Figure 3: Radion 4D potential in the case of different input masses of Dirac neutrinos: $m_2$ =6.7, 7.7, 8.7, 9.7, 10.7 $\times 10^{-3}eV$, while $m_3$ = 5.8$\times 10^{-2}eV$, $\Lambda_5=3\times 10^{-12}$ and $r^2=107 eV^{-2}$.
• Figure 4: Radion field effective potential under three different value of $\left\langle \phi \right\rangle$: 0, $2\times 10^{-2}$, $5\times 10^{-2}$. In the plot we set $r^2=107 eV^{-2}$ and neutrino masses in normal hierarchy with $m_1=0$ as before, and take $\Lambda_{\phi}=2.68\times 10^{-11} eV^5$.