二次爱因斯坦-嘉当引力中狄拉克诱导挠率的色引力波检验：纳赫兹脉冲星计时阵列零信号特征
Chromatic Gravitational-Wave Tests of Dirac-Induced Torsion in Quadratic Einstein--Cartan Gravity: Nanohertz PTA Null Signatures
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中文总结 AI 辅助
本研究在二次爱因斯坦-嘉当-狄拉克引力中推导了张量传播的条件性结果，证明在特定平均场闭合下无挠率色散效应，并定义了用于脉冲星计时阵列的零检验统计量。
中文摘要 AI 辅助
我们推导了具有宇称偶不变式 $\zeta T_{\lambda\mu\nu} T^{\lambda\mu\nu}$ 和由粗粒化费米子轴矢量流产生的代数挠率的爱因斯坦-嘉当-狄拉克引力中主导张量传播的条件性结果。在空间平坦、均匀且各向同性的背景上，若物质态满足显式的因子化平均场闭合条件，则消除非动力学洛伦兹联络会在主导二阶导数阶产生爱因斯坦-希尔伯特横无迹（TT）作用：$\langle J_{5\mu}J_5^{\mu}\rangle$ 的连通贡献设为零，因子化标量 $\bar J_{5\mu}\bar J_5^\mu$ 的一阶和二阶 TT 响应为零，且固有 TT 各向异性应力为零。在这些条件下，$Q_T= M_{\rm Pl}^{2}$，张量速度为光速，局域色散关系为 $\omega^2=k_{\rm phys}^2$，没有主导的传播诱导偏振分裂。该贡献是针对该不变式的特定模型约束 TT-黑塞计算，保留了辅助联络响应，并陈述了使 $\zeta$ 相关项抵消所需的闭合条件。一般费米子态的连通流 TT 响应未被评估；因此这是一个条件性结果，而非一般爱因斯坦-嘉当不可行定理。耦合 $\zeta$ 保留在轴-轴费米子接触相互作用中。我们为未来脉冲星计时阵列（PTA）似然分析定义了零检验可观测量和协方差加权统计量。已发表的 NANOGrav 15 年谐波后验和公开的 2026 年合作预印本仅用作一致性检验：我们不进行新的到达时间（TOA）级似然或证据计算，这些数据不直接约束 $\zeta$。
英文摘要
We derive a conditional result for leading tensor propagation in Einstein--Cartan--Dirac gravity with the parity-even invariant $ζT_{λμν} T^{λμν}$ and algebraic torsion sourced by a coarse-grained fermionic axial current. On a spatially flat, homogeneous, and isotropic background, eliminating the nondynamical Lorentz connection yields the Einstein--Hilbert transverse-traceless (TT) action at leading two-derivative order if the matter state obeys an explicit factorized mean-field closure: the connected contribution to $\langle J_{5μ}J_5^μ\rangle$ is set to zero, the factorized scalar $\bar J_{5μ}\bar J_5^μ$ has vanishing first- and second-order TT response, and intrinsic TT anisotropic stress vanishes. Under these conditions, $Q_T= M_{\rm Pl}^{2}$, the tensor speed is luminal, and the local dispersion relation is $ω^2=k_{\rm phys}^2$, with no leading propagation-induced polarization splitting. The contribution is a model-specific constrained TT-Hessian calculation for this invariant that retains the auxiliary-connection response and states the closure needed for the $ζ$-dependent terms to cancel. The connected-current TT response of a general fermionic state is not evaluated; this is therefore a conditional result, not a general Einstein--Cartan no-go theorem. The coupling $ζ$ remains in the axial--axial fermion contact interaction. We define null-test observables and a covariance-weighted statistic for future pulsar-timing-array (PTA) likelihood analyses. Published NANOGrav 15-year harmonic posteriors and the public 2026 collaboration preprint serve only as consistency checks: we perform no new time-of-arrival (TOA)-level likelihood or evidence calculation, and these data do not directly constrain $ζ$.
发表机构
- State Key Laboratory of Radio Astronomy and Technology, Xinjiang Astronomical Observatory, CAS（中国科学院新疆天文台射电天文与技术国家重点实验室）
- Shanxi Province Intelligent Optoelectronic Sensing Application Technology Innovation Center, Yuncheng University（运城学院山西省智能光电传感应用技术创新中心）
- College of Mechanical and Electrical Engineering, Tarim University（塔里米大学机电工程学院）
- Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University（北京师范大学天文与前沿物理研究所）
- School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院）
- Departamento de Física Teórica, IF-UERJ（里约热内卢联邦大学理论物理系）
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