AI 中文总结
该研究提出毕安基I型背景下哈勃张力检验的定量框架，推导弱剪切轴对称映射关系，发现仅含剪切的模型无法解决哈勃张力，为利用SNe、BAO等检验晚时间各向异性提供可证伪方案。
AI 中文摘要
哈勃张力通常被表述为各向同性FLRW模型中对单一标量参数H₀的两种测定结果之间的不一致。我们开发了一个定量框架，将该张力视为对均匀、各向异性膨胀的毕安基I型（Bianchi type I）背景下宇宙学数据的标量FLRW压缩的一致性检验。除综合毕安基I型运动学、类光测地线及光学传播的已有结果外，我们的原创贡献是完成了弱剪切、轴对称计算，将特定的剪切历史映射为低红移光度距离四极矩。该计算明确区分了依赖方向的红移——仿射参数映射与雅可比聚焦贡献，通过解析极冠玩具窗口传播所得的距离四极矩。对于自由衰减剪切，我们得到A_D(z) = -B_{H0} + (2q₀-1)B_{H0}z/2 + (5-q₀-18q₀²+6j₀)B_{H0}z²/12 + O(z³, B_{H0}²)，其中B_{H0}=(H_{∥0}-H_{⊥0})/H₀，j₀为平均急动参数。代表性的大爆炸核合成（BBN）极限Ω_{σ0} ≤ 10⁻²³，意味着|B_{H0}| ≤ 9.5×10⁻¹²，且z=0.15处的距离模数四极矩低于2.4×10⁻¹¹ mag。所用的早期宇宙约束来自前期工作；其新颖之处在于将该约束通过推导的萨克斯-雅可比（Sachs--Jacobi）映射传播为对光度距离四极矩和星表窗口偏差的约束。相比之下，1%的方向偏移需要Ω_{σ0}≈2.5×10⁻⁵，而匹配普朗克2018年与SH0ES 2022年的分离则需要Ω_{σ0}≈1.8×10⁻³。因此，仅含剪切的最小模型无法解决该张力，不过该框架为利用超新星（SNe）、重子声学振荡（BAO）和标准汽笛检验晚时间各向异性提供了可证伪的方案。
英文摘要
The Hubble tension is usually formulated as a disagreement between two determinations of a single scalar parameter, $H_0$, within an isotropic FLRW model. We develop a quantitative framework treating the tension as a consistency test of the scalar FLRW compression of cosmological data in a homogeneous, anisotropically expanding Bianchi type I background. Beyond synthesizing established results on Bianchi I kinematics, null geodesics, and optical propagation, our original contribution is a worked weak-shear, axisymmetric calculation mapping a specified shear history into a low-redshift luminosity-distance quadrupole. The calculation explicitly separates the direction-dependent redshift--affine-parameter mapping from the Jacobi-focusing contribution, propagating the resulting distance quadrupole through an analytic polar-cap toy window. For freely decaying shear, we obtain $A_D(z) = -B_{H0} + (2q_0-1)B_{H0}z/2 + (5-q_0-18q_0^2+6j_0)B_{H0}z^2/12 + O(z^3, B_{H0}^2)$, where $B_{H0}=(H_{\parallel 0}-H_{\perp 0})/H_0$ and $j_0$ is the mean jerk parameter. A representative BBN limit, $Ω_{σ0} \le 10^{-23}$, implies $\vert{}B_{H0}\vert{} \le 9.5 \times 10^{-12}$ and a distance-modulus quadrupole below $2.4 \times 10^{-11}$ mag at $z=0.15$. The early-Universe bound used is adopted from prior work; the novelty lies in propagating it through the derived Sachs--Jacobi mapping into limits on the luminosity-distance quadrupole and catalogue-window bias. By contrast, a 1% directional shift requires $Ω_{σ0} \approx 2.5 \times 10^{-5}$, while matching the Planck 2018--SH0ES 2022 separation requires $Ω_{σ0} \approx 1.8 \times 10^{-3}$. Thus, the minimal shear-only model cannot resolve the tension, though the framework supplies a falsifiable programme for testing late-time anisotropy with SNe, BAO, and standard sirens.
Comments59 pages, 3 figures
Journal refUniverse, 12, 232 (2026)
