Tomoki Katayama | Searcharxiv

arXiv2026

Casimir-Induced Quintessence in Dark Dimension

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 $D_M/r_d$.

gr-qc↗

arXiv2025

A New Definition of Horndeski Theory and the Possibility of Multiple Scalar Field Extensions

In the single-field case, Horndeski provides the most general scalar-tensor theory with second-order field equations. By contrast, systematic multi-field extensions remain incomplete: while the general field equations for the bi-Horndeski case are known, a general action has not been established, and for cases with three or more fields, neither a general action nor general equations are available. We characterize Horndeski theory by three mild axioms: closure under invertible pure disformal transformations, the inclusion of a minimal Horndeski theory as an anchor, and the requirement that the coefficient functions of the Lagrangian be arbitrary up to relations required by the closure. Under this characterization, we recover the standard single-field action up to boundary terms and obtain a practical path to multi-field constructions. In particular, we show that antisymmetric structures, such as those identified by E. Allys, S. Akama, and T. Kobayashi, appear within this framework, and indicate that this viewpoint has the potential to account for features captured by known bi-Horndeski equations.

gr-qc↗