What question did this study set out to answer?

This work aims to demonstrate that the Hubble Tension is a scaling artifact, not a sign of new physics.

July 14, 2026Open Access

Non-Linear Derivation of the Effective Matter Density under the Unified Causal Principle (UCP) and Resolution of the Hubble Tension as a Scaling Artifact

Key Points

This work aims to demonstrate that the Hubble Tension is a scaling artifact, not a sign of new physics.
Derivation of effective matter and dark energy densities using UAT/UCP frameworks.
Incorporated constants and observational inputs independent of ΛCDM.
Established physical interpretations for each component in the effective density equation.
Derived Ω_m = 0.3133 and Ω_Λ = 0.6867, closely matching Planck values with differences of 0.55% and 0.24%.
Recalibrated Planck baryon density agrees with first-principles BBN, showing a 15% discrepancy linked to H₀ scaling.
Results imply dark matter may be a byproduct of baryonic matter interactions, and dark energy is a geometric feature.

Abstract

This submission presents a formal first-principles derivation demonstrating that the observational discrepancy known as the "Hubble Tension" is not indicative of new particle physics, but rather a scaling artifact arising from the application of a linear model (ΛCDM) to a non-linear causal topology. Using the Unified Applicable Time (UAT) and Unified Causal Principle (UCP) frameworks, we derive the effective matter density (Ωₘ) and the dark energy density (Ω_Λ) from first principles, without recourse to free fitting parameters or ΛCDM-derived inputs. Methodology: The derivation uses three UAT/UCP constants (the Ivancho limit κcrit = 4. 978, the golden ratio φ ≈ 1. 618, and the thermal calibration margin φ*/η = 0. 07), three observational inputs independent of ΛCDM (TCMB = 2. 7255 K from COBE/FIRAS, ηB = 6. 1×10⁻¹⁰ from Big Bang Nucleosynthesis, and H₀ = 73. 04 km/s/Mpc from SH0ES), and standard physics (the Stefan-Boltzmann law, the blackbody photon distribution, and BBN abundances). Key equation: The effective matter density is derived as Ωₘ (eff) = Ωb × κcrit × φ × (1 - φ*/η). Each factor has a precise physical interpretation: Ωb is the bare baryon density from BBN, κcrit is the maximum causal amplification (Ivancho limit), φ is the geometric phase resonance (golden ratio), and (1 - 0. 07) is the efficiency after thermal dissipation. The dark energy density follows from geometric closure under the UAT prediction of exact spatial flatness: Ω_Λ = 1 - (Ωₘ + Ωᵣ). Results: The derived values (Ωₘ = 0. 3133, Ω_Λ = 0. 6867) match the Planck 2018 consensus values (Ωₘ = 0. 315 ± 0. 007, Ω_Λ = 0. 685 ± 0. 007) with differences of 0. 55% and 0. 24% respectively. The apparent discrepancy in Ωb (15%) is shown to be a direct consequence of the H₀ scaling effect: recalibrating the Planck baryon density from H₀ = 67. 36 to H₀ = 73. 04 km/s/Mpc yields Ωb ≈ 0. 0419, in agreement with the first-principles BBN calculation (0. 04182). Implications: The results suggest that dark matter may not be an exotic particle but rather the causal friction imprint of baryonic matter, amplified by the geometric structure of the causal network. Dark energy emerges not as a fundamental constant but as the geometric remainder under exact spatial flatness. The Hubble Tension is resolved as a metric calibration artifact. The package includes the LaTeX manuscript and the Python script that reproduces all calculations.

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