2026/07/31 by Luigi Tedesco
Physics and Astronomy · #astro-ph.CO #gr-qc #hep-ph #hep-th
59 pages, 3 figures
arxiv created 2026/07/31 · arxiv updated 2026/08/03
The Hubble tension is usually formulated as a disagreement between two determinations of a single scalar parameter, H0, 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 AD(z) = -BH0 + (2q0-1)BH0z/2 + (5-q0-18q02+6j0)BH0z2/12 + O(z3, BH02), where BH0=(H∥ 0-H⊥ 0)/H0 and j0 is the mean jerk parameter. A representative BBN limit, Ωσ0 ≤ 10-23, implies \vertBH0\vert ≤ 9.5 × 10-12 and a distance-modulus quadrupole below 2.4 × 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 Ωσ0 ≈ 2.5 × 10-5, while matching the Planck 2018--SH0ES 2022 separation requires Ωσ0 ≈ 1.8 × 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.