What question did this study set out to answer?

The research aims to derive the cosmic dark matter-to-baryon density ratio using Shannon's entropy and Born's rule.

February 22, 2026Open Access

Derivation of the Cosmic Dark Matter Ratio from Shannon Entropy and Born's Rule

Key Points

The research aims to derive the cosmic dark matter-to-baryon density ratio using Shannon's entropy and Born's rule.
Utilized Shannon's entropy uniqueness theorem and Born's rule.
Derived a logarithmic scalar field from baryonic probability amplitudes.
Analyzed data from 175 SPARC galaxies using Landauer erasure.
Derived dark matter-to-baryon density ratio of approximately 5.437, consistent with Planck data.
Interpolation function outperformed MOND baseline at a significant level (5.9σ).
Thermodynamic predictions matched cluster lensing mass ratios within 3% of observational data.

Abstract

A conditional derivation of the cosmic dark matter-to-baryon density ratio from Shannon's entropy uniqueness theorem and Born's rule. The normalized baryonic probability amplitude sources a logarithmic scalar field whose entropy critical point yields the ratio 2e ≈ 5.437, consistent with Planck at 1.1σ. Landauer erasure and the Euclidean on-shell action amplitude yield a fully derived, zero-parameter interpolation function that outperforms the standard MOND baseline on 175 SPARC galaxies at 5.9σ. The thermodynamic equilibrium prediction for cluster lensing mass ratios matches observations to 3%, and the background CMB cosmology is indistinguishable from ΛCDM at current precision.

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