AI 中文总结
本文扩展了基于紧致额外维度各向异性标度的宇宙学常数问题框架，引入z=1形变恢复紧致方向动力学，验证了真空能抵消性，同时指出需额外谱条件消除体自由度产生的拓扑敏感卡西米尔贡献。
AI 中文摘要
我们此前提出了一种基于紧致额外维度中各向异性标度的宇宙学常数问题新方法。在超局域 $z=0$ 极限下，可投影 lapse、保持叶状结构的微分同胚以及高阶形式通量之间的相互作用，使得引力场方程对物质真空能的辐射修正不敏感。本文将该框架扩展至超局域极限之外，引入 $z=1$ 形变以恢复紧致方向的动力学。我们表明，真空能抵消在背景方程层面仍成立，而一般的外曲率耦合会传播出一个额外的标量鬼场。健康的二次谱在这些耦合间选出了Fierz-Pauli关系，这为用五维爱因斯坦引力、一个顶形式通量以及一个类空khoron标量场实现提供了动机，该标量场可动态定义一个优选的可投影叶状结构。在该协变表述中，全局约束源于khoron叶空间上的辅助einbein，且重整化后的物质真空能的常数项会从内禀爱因斯坦方程中代数地抵消。最后，允许物质在紧致维度周围传播会产生有限的、对拓扑敏感的卡西米尔贡献，这些贡献不会被该机制自动消除，抑制这些贡献需要对传播的体自由度施加额外的谱条件。
英文摘要
We have previously proposed a new approach to the cosmological constant problem based on anisotropic scaling in a compact extra dimension. In the ultra-local $z=0$ limit, the interplay between a projectable lapse, foliation-preserving diffeomorphisms, and higher-form fluxes renders the gravitational field equations insensitive to radiative corrections to the matter vacuum energy. Here we extend this framework beyond the ultra-local limit by introducing $z=1$ deformations that restore dynamics along the compact direction. We show that vacuum-energy cancellation persists at the level of the background equations, while generic extrinsic-curvature couplings propagate an additional scalar ghost. A healthy quadratic spectrum selects the Fierz-Pauli relation between these couplings. This motivates a particularly simple realization in terms of five-dimensional Einstein gravity, a top-form flux, and a spacelike khoron scalar field that dynamically defines a preferred projectable foliation. In this covariant formulation, the global constraint arises from an auxiliary einbein on the space of khoron leaves, and constant shifts of the renormalized matter vacuum energy cancel algebraically from the intrinsic Einstein equations. Finally, allowing matter to propagate around the compact dimension generates finite, topology-sensitive Casimir contributions that are not automatically removed by the mechanism. Suppressing these contributions requires additional spectral conditions on the propagating bulk degrees of freedom.
Comments27 pages, follow-up to [2604.08659]
