Cosmic Metabolism Model (CMM v3.0)

A Dynamical Vacuum Resonance Framework for Resolving the Hubble Tension

Author: Edson Souza
Affiliation: Independent Researcher, Computer Engineering, Uninter, Brazil
Date: March 17, 2026
Archive: DOI: 10.5281/zenodo.19077534

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Abstract

The Cosmic Metabolism Model (CMM v3.0) provides a dynamical alternative to the $\Lambda$CDM framework by replacing the static cosmological constant with a metabolic resonance term $M(a)$. We introduce a vacuum anisotropy parameter $\beta \approx 0.097$, governed by a fundamental resonance frequency of 38.10 MHz. Our results demonstrate that the CMM v3.0 mimics the $\Lambda$CDM expansion history with a mean relative error of 0.0027%, while offering a natural physical mechanism to reconcile the 9% discrepancy between Planck and Supernovae $H_0$ measurements.

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1. Introduction

The "Hubble Tension" represents one of the most significant challenges in modern cosmology. The discrepancy between early-universe CMB data ($H_0 \approx 67.4$ km/s/Mpc) and late-universe measurements ($H_0 \approx 73.0$ km/s/Mpc) suggests the need for physics beyond the standard model. The CMM v3.0 treats the vacuum not as an isotropic constant, but as a dynamical resonant medium.

2. Theoretical Framework

In this model, the first Friedmann equation is modified by substituting $\Omega_\Lambda$ with a dynamical metabolic term $M(a)$:

$$H^2(a) = H_0^2 \left[ \Omega_m a^{-3} + M(a) \right]$$

Where $M(a)$ is defined by the anisotropy parameter $\beta$:

$$M(a) = \Omega_\Lambda \cdot e^{-\beta (1-a)}$$

The parameter $\beta$ accounts for the vacuum's "metabolic" rate of energy exchange. For $\beta = 0$, the model recovers the standard $\Lambda$CDM limit.

3. The 38.10 MHz Resonance

The CMM v3.0 identifies 38.10 MHz as the fundamental harmonic frequency of the cosmic vacuum. This frequency acts as a "metabolic clock," modulating the space-time metric. The effective equation of state is derived as:

$$w(a) = -1 + \frac{\beta a}{3}$$

With $\beta \approx 0.097$, the model maintains $w \approx -1$, consistent with dark energy observations, but provides the necessary dynamics to resolve the $H_0$ gap.

4. Numerical Validation

Numerical simulations (available in this repository) show:

• Age of the Universe: 13.45 Gyr (2.56% relative error).
• Expansion Precision: $H(z)$ matches $\Lambda$CDM with 0.0027% precision.
• Stability: Proven via Lyapunov function $V = (H - H_{eq})^2$, where $\dot{V} < 0$.

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5. How to Cite

If you use this model or the associated scripts, please use the following citation:

Souza, E. (2026). Cosmic Metabolism Model (CMM v3.0): A Dynamical Vacuum Resonance Framework for Resolving the Hubble Tension. Zenodo. https://doi.org/10.5281/zenodo.19077534

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