发表机构
Departamento de Física, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional（墨西哥国立理工学院高级研究中心物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在共形规范下对Weyl不变引力进行正则量子化，产生几何宇宙学常数项，驱动w=-1的加速膨胀，并从第一性原理推导出CMaDE假说，解决了宇宙巧合问题。
AI 中文摘要
我们在特定的共形规范下对Weyl不变引力进行了正则量子化。将尺度因子固定为 $a(\eta) = 1/(H_0\eta)$ 会在爱因斯坦方程左侧产生一个有效的几何宇宙学常数项 $\mathcal{M}(\eta) = \alpha/\eta^2$，从而在构造上保证了状态方程 $w = -1$。Bianchi恒等式要求存在一个补偿标量场；我们证明该补偿场就是度规的共形模，是一种规范人为产物，在完整的量子理论中不会传播鬼魂不稳定性。我们发展了完整的ADM哈密顿形式体系，并证明了约束代数以标准第一类形式闭合。正则量子化产生了一个良定义的Wheeler-DeWitt方程，其中 $\mathcal{M}(\eta)$ 项作为势垒动态抑制小尺度宇宙的量子产生。我们证明了物理约化哈密顿量从下方有界，时间演化在物理希尔伯特空间中严格幺正，并且微观因果性得以保持。在纯真空区域，该模型允许精确解析解，其中 $\Omega_{\text{DE}} = 1$，无需精细调节参数即可解决宇宙巧合问题。在物质主导时期，共动视界尺度为 $R_H \propto \eta$，因此我们的结果 $\mathcal{M} \propto \eta^{-2} \propto R_H^{-2}$ 从第一性原理重现了中心康普顿质量暗能量（CMaDE）假说，并确立了 $n = -2$ 作为共形全息暗能量（CHDE）参数化 $\mathcal{M} \propto \eta^n$ 的理论基准。从纯共形对称原理出发，该模型提供了一个有效的几何宇宙学常数项，驱动着具有 $w = -1$ 的加速膨胀，为CMaDE提供了缺失的作用原理。
英文摘要
We present the canonical quantization of Weyl-invariant gravity in a specific conformal gauge. Fixing the scale factor as $a(η) = 1/(H_0η)$ yields an effective geometric cosmological term $\mathcal{M}(η) = α/η^2$ on the left-hand side of the Einstein equations, guaranteeing an equation of state $w = -1$ by construction. The Bianchi identity requires a compensator scalar field; we show that this compensator is the conformal mode of the metric, a gauge artifact that does not propagate ghost instabilities in the full quantum theory. We develop the complete ADM Hamiltonian formulation and prove that the constraint algebra closes in standard first-class form. Canonical quantization yields a well-defined Wheeler-DeWitt equation where the $\mathcal{M}(η)$ term acts as a potential barrier dynamically suppressing the quantum creation of small-scale universes. The physical reduced Hamiltonian is demonstrated to be bounded from below, time evolution is strictly unitary in the physical Hilbert space, and microcausality is preserved. In the pure vacuum regime, the model admits an exact analytical solution with $Ω_{\text{DE}} = 1$, resolving the cosmic coincidence problem without fine-tuned parameters. In the matter-dominated era, the comoving horizon scales as $R_H \propto η$, so our result $\mathcal{M} \propto η^{-2} \propto R_H^{-2}$ reproduces the central Compton Mass Dark Energy (CMaDE) hypothesis from first principles and establishes $n = -2$ as the theoretical benchmark for the Conformal Holographic Dark Energy (CHDE) parametrization $\mathcal{M} \propto η^n$. From a pure conformal symmetry principle, the model delivers an effective geometric cosmological term that drives the accelerated expansion with $w = -1$, providing the missing action principle for CMaDE.
DOI：10.1088/1361-6382/ae9de4 10.1088/1361-6382/ae9de4 10.1088/1361-6382/ae9de4
