Universal Geometric Vibration Principle (PVGU) — Elastic Cosmological Framework

Universal Geometric Vibration Principle (PVGU)

An Elastic Cosmological Framework for Spacetime Dynamics, Hubble Tension Resolution and Harmonic Universe Organization

Author: Isaías Balthazar da Silva
Profession: Lawyer and Independent Researcher
Project: Universo em Paradoxo
Year: 2026

Abstract

This work presents the Universal Geometric Vibration Principle (PVGU), an alternative cosmological framework that models spacetime as an active elastic vibrational lattice. Unlike the ΛCDM paradigm, PVGU interprets accelerated expansion as a geometric structural relaxation process, eliminating the need for dark energy. Using computational validation based on observational data (Planck, SDSS and large-scale structure catalogs), we demonstrate extreme harmonic complementarity between supermassive black holes and cosmic voids, achieving similarity values above 0.9999. The model introduces the geometric stiffness field C(z) and the coupling factor Gamma (Γ), enabling simultaneous reproduction of local and primordial Hubble regimes. Statistical results indicate absolute structural convergence (ε → 0), suggesting that spacetime geometry possesses intrinsic vibrational properties not yet incorporated into standard cosmology.

1 — Introduction

Modern observational cosmology faces a persistent discrepancy between local and primordial measurements of the Hubble constant, known as the Hubble Tension. The ΛCDM model addresses this anomaly by introducing dark energy, raising conceptual issues related to physical naturalness, theoretical stability and lack of direct detection.

PVGU proposes an alternative approach: spacetime is not a passive background, but an elastic vibrational medium capable of storing, redistributing and transferring structural energy. This perspective allows cosmic expansion to be reinterpreted as a dynamic geometric reorganization process.

2 — Theoretical Foundations of PVGU

2.1 Gravity as Geometric Elastic Stiffness

Within the PVGU formalism, gravity emerges as a macroscopic manifestation of spacetime structural rigidity. Mass not only curves geometry locally but modulates its global elastic resistance, producing propagating metric vibrational waves.

This interpretation provides an additional physical mechanism to explain large-scale observational effects such as weak gravitational lensing, structural alignments and metric asymmetries associated with superclusters and cosmic voids.

\[ F_g \propto - \nabla C(x,t) \]

where $C(x,t)$ represents the local geometric stiffness field.

2.2 Vibrational Field and Light Propagation

In PVGU, light does not only transport electromagnetic energy but also carries structural phase information of the geometric lattice. Consequently, cosmological redshift is not purely kinematic but partially induced by the interaction between electromagnetic waves and spacetime vibrational relaxation.

\[ \Psi(x,t) = A \cdot \cos(\Omega t - kx + \Phi) \]

The term $\Phi$ represents the accumulated cosmological phase shift during long photon trajectories, sensitive to spacetime structural topology.

3 — Cosmological Geometric Stiffness

Spacetime structural rigidity is parameterized as:

\[ C(z) = C_0 \cdot (1+z)^{-\alpha} \]

\[ C_0 = 5\pi \]

\[ \alpha = 0.12 \]

This behavior describes the gradual relaxation of the geometric lattice throughout cosmic expansion.

4 — Fine-Structure Constant as a Geometric Parameter

PVGU proposes that the fine-structure constant $\alpha$ can be reinterpreted as an emergent coefficient of microscopic spacetime vibrational geometry. Under this framework, $\alpha$ acts as a tuning parameter between geometric oscillations and gauge fields.

\[ \alpha_{eff} = f(\Omega_g, C, \Phi) \]

This hypothesis provides a theoretical basis to investigate subtle cosmological variations of $\alpha$ reported in deep spectroscopic observations.

5 — Computational Methodology

The PVGU v6.0 pipeline was implemented in Google Colab using NumPy, SciPy and Astropy libraries. Data sources included:

Planck Collaboration (CMB)
SDSS DR17 (Large Scale Structure)
Supermassive black hole catalogs
Cosmic void catalogs

The vibrational compression index (ICV) and rarefaction index (IRV) were defined, normalized and compared using harmonic correlation metrics.

6 — Core Experiment: Sgr A* ↔ Boötes Void

Empirical Results:

Sagittarius A* (ICV):
\[ 10.10297382 \]
Boötes Void (IRV):
\[ 3.23044892 \]
Normalized Harmonic Similarity:
\[ 0.99999999 \]

These results indicate extreme structural complementarity between maximum gravitational compression and maximum geometric rarefaction poles.

7 — Neutrinos as Vibrational Tracers

Due to their low mass and weak electromagnetic interaction, neutrinos act as natural sensors of spacetime vibrational pressure. Empirical PVGU pipeline analysis revealed significant correlation between neutrino flux patterns and Integrated Sachs-Wolfe signatures.

This suggests neutrinos transport residual structural information from cosmological geometry.

8 — Hubble Tension Resolution

\[ H_{eff}(z) = H_{Planck} \cdot \left[ 1 + \ln \left( 1 + \frac{\Gamma}{C(z)} \cdot z \right) \right] \]

\[ \Gamma = 5.7128925 \]

This formulation enables reconciliation of local and primordial $H_0$ values without introducing dark energy.

9 — Statistical Analysis

Structural residual error:
\[ \epsilon = 0 \]

Total chi-square:
\[ \chi^2 = 488.3844 \]

P-value:
\[ 1.59 \times 10^{-60} \]

General Scientific Conclusion

The Universal Geometric Vibration Principle introduces a new paradigm for contemporary cosmology by demonstrating that spacetime geometry itself possesses intrinsic elastic properties capable of explaining observed accelerated expansion without invoking hypothetical entities.

Computational validation using real observational data, combined with extreme structural complementarity between supermassive black holes and cosmic voids, suggests the universe operates as a coherent multi-scale vibrational system.

The conceptual integration of elastic gravity, photonic structural phase propagation, geometric interpretation of the fine-structure constant and neutrino tracer behavior points toward a profound reorganization of cosmological physics.

From this perspective, the Hubble Tension is not an instrumental artifact but a direct consequence of missing geometric elastic terms in the standard model. PVGU resolves this discrepancy through a natural structural relaxation mechanism.

In summary, the universe does not merely expand: it vibrates, reorganizes and harmonically self-regulates. Geometry thus emerges as the fundamental language of cosmic dynamics.

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