March 3, 2026Open Access

Topological Horizon Lensing as a Solution to High-Redshift Hubble Tension: A Bayesian Analysis

Key Points

High-redshift Hubble tension results from a systematic deviation in luminosity distance, suggesting new physics.
Decisive Bayesian evidence supports the τCDM model over the traditional ΛCDM model, with ΔBIC > 300.
Machine learning using a Gated Residual Network identifies this deviation, enhancing our understanding of cosmic expansion.
The framework proposes a connection between cosmic lensing effects and galactic acceleration, hinting at a unified Dark Sector.

Abstract

The ΛCDM model, while successful at explaining Cosmic Microwave Background (CMB) anisotropies, faces increasing tension with late-universe observations, particularly regarding the Hubble constant (H0) and high-redshift expansion rates. In this work, we present a phenomenological correction to the luminosity distance relation derived from a "blind" machine learning analysis of over 4, 000 cosmological objects, including Type Ia Supernovae (Pantheon+), Baryon Acoustic Oscillations (BAO), Quasars, and Gamma-Ray Bursts. Using a Gated Residual Network (GatedResNet) optimized with a robust Cauchy loss function to mitigate outliers, we detect a systematic deviation in the distance modulus at z > 1 of magnitude Δμ ≈ -0. 18 log (1+z). Bayesian model comparison yields decisive evidence (ΔBIC > 300, Bayes Factor K > 10⁶0) favoring this correction over the standard ΛCDM model. We interpret this signal not as an evolution of Dark Energy, but as a "Container Lensing" effect: a topological magnification induced by a conformal inversion boundary condition at the cosmic horizon. We term this framework τCDM (Topological Cold Dark Matter). Furthermore, we report a numerical coincidence where the lensing amplitude A ≈ 0. 18 relates the cosmic acceleration scale to the galactic critical acceleration (a0), suggesting a path toward a unified Dark Sector theory (Pure-τ). Key Contributions: Blind Discovery: Identification of a systematic high-redshift deviation using scientific machine learning (GatedResNet) without assuming a background cosmology. Statistical Evidence: Overwhelming Bayesian support (ΔBIC ≈ +320) for the τCDM model over ΛCDM using a combined dataset of 2, 852 probes. The τCDM Framework: A geometric resolution to the Hubble Tension via Topological Horizon Lensing, explaining the bifurcation between distance probes (SNe, BAO, QSO) and clock probes (CC). Unified Dark Sector: A numerical link connecting the cosmic lensing amplitude (A ≈ 0. 18) with the MOND acceleration scale (a0), suggesting Dark Matter may be an inertial effect of the global topology.

Topological Horizon Lensing as a Solution to High-Redshift Hubble Tension: A Bayesian Analysis

Key Points

Abstract

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