A Quantitative Framework for Testing the Hubble Tension in a Bianchi Type I Cosmological Background

Abstract

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, ${\Omega }_{\sigma 0}\le 10^{-23}$, implies $|B_{H0}|\le 9.5\times 10^{-12}$ 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 ${\Omega }_{\sigma 0}\approx 2.5\times 10^{-5}$, while matching the Planck 2018--SH0ES 2022 separation requires ${\Omega }_{\sigma 0}\approx 1.8\times 10^{-3}$. 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.

59 pages, 3 figures

References in corpus (52)

• Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies
• A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km/s/Mpc Uncertainty from the Hubble Space Telescope and the SH0ES Team
• In the Realm of the Hubble tension $-$ a Review of Solutions
• Bayes in the sky: Bayesian inference and model selection in cosmology
• A gravitational-wave standard siren measurement of the Hubble constant
• Tensions between the Early and the Late Universe
• A 6% measurement of the Hubble parameter at $z\sim 0.45$: direct evidence of the epoch of cosmic re-acceleration
• Information criteria for astrophysical model selection
• Constraining Cosmological Parameters Based on Relative Galaxy Ages
• The Hubble Hunter's Guide
• Precision big bang nucleosynthesis with improved Helium-4 predictions
• Big-Bang Nucleosynthesis After Planck
• Planck 2018 results. III. High Frequency Instrument data processing and frequency maps
• CMB Anomalies after Planck
• Is the Observable Universe Consistent with the Cosmological Principle?
• Evidence for anisotropy of cosmic acceleration
• Cosmic Microwave Background Quadrupole and Ellipsoidal Universe
• Ellipsoidal Universe Can Solve The CMB Quadrupole Problem
• Anisotropic Dark Energy: Dynamics of Background and Perturbations
• Light-cone averaging in cosmology: formalism and applications
• Anisotropic Cosmological Constant and the CMB Quadrupole Anomaly
• Constraints on a Bianchi type I spacetime extension of the standard $\Lambda$CDM model
• Probing the isotropy of cosmic acceleration traced by Type Ia supernovae
• Probing cosmic anisotropy with gravitational waves as standard sirens
• An exact Jacobi map in the geodesic light-cone gauge
• Testing the isotropy of the Universe by using the JLA compilation of type-Ia supernovae
• Testing spatial curvature and anisotropic expansion on top of the $\Lambda$CDM model
• Probing Dark Energy Anisotropy
• Fractal universe and cosmic acceleration in a Lemaître-Tolman-Bondi scenario
• Anisotropy of Cosmic Acceleration
• Anisotropic dark energy and ellipsoidal universe
• Cosmic Parallax: possibility of detecting anisotropic expansion of the universe by very accurate astrometry measurements
• A new approach to the propagation of light-like signals in perturbed cosmological backgrounds
• Geodesic-light-cone coordinates and the Bianchi I spacetime
• The Local Distance Network: a community consensus report on the measurement of the Hubble constant at 1% precision
• Percent-Level Test of Isotropic Expansion Using Type Ia Supernovae
• Cosmic Parallax in Ellipsoidal Universe
• The Ellipsoidal Universe in the Planck Satellite Era
• Can Cosmic Parallax Distinguish Between Anisotropic Cosmologies?
• Constraints on an Anisotropic Universe
• Testing the isotropy of cosmic acceleration with Pantheon+ and SH0ES: A cosmographic analysis
• Anisotropy in Pantheon+ supernovae
• Colloquium: The Cosmic Dipole Anomaly
• Testing anisotropic Hubble expansion
• Anisotropic universe with anisotropic dark energy
• An Anisotropic Model for the Universe
• Inhomogeneous and anisotropic Universe and apparent acceleration
• Hubble Diagrams in Statistically Homogeneous, Anisotropic Universes
• Updated Cosmological Constraints from 2D BAO Measurements: A New Compilation and Comparison with DESI DR2
• The Chicago Carnegie Hubble Program: Improving the Calibration of SNe Ia with JWST Measurements of the Tip of the Red Giant Branch
• Ellipsoidal Universe and Cosmic Shear
• Constraining Axially Symmetric Bianchi Type I Model with Self-Consistent Recombination History and Observables