Quantum Vibrational Relativity (QVR): A Unified Framework Bridging General Relativity, Quantum Mechanics, and Cosmology

Quantum Vibrational Relativity (QVR) - Version 2.0

Overview:

A scalar-field extension of General Relativity in which a single k-essence field with conformal coupling to matter replaces both dark matter particles and a separate cosmological constant. The field's kinetic function F(Y) = Y + (2/3)Y^{3/2} exp(λY) produces a natural phase transition: pressureless dust (CDM-like) during matter domination, MOND-like modified gravity at late times.

What's new in Version 2:

• Dynamical Phase Transition: Formalized the $\exp(\lambda Y)$ mechanism to reproduce CMB acoustic peaks without dark matter.

• Expanded Precision Suite: Documented margins for Cassini PPN ($10^{11}\times$), binary pulsars ($10^{22}\times$), and BBN ($10^3\times$).

• Wide Binary Resolution: Theoretical prediction of 1.6% velocity boost, reducing the Banik et al. (2024) tension to $0.3\sigma$.

• Explicit BBN Proof: Calculation of $\delta G/G = 1.7 \times 10^{-6}$ during nucleosynthesis using the stress-energy trace identity.

• Attractor Dynamics: Dynamical resolution of the Cosmic Coincidence problem ($\Omega_m \to 1/3, \Omega_\Lambda \to 2/3$).

Seven-pillar validation:

1. Cosmological–galactic unification: κ = 1.063, 95% CI [0.908, 1.200]
2. Pantheon+ SNe oscillation: 823 Myr period at 3.5σ
3. Wavefunction localization via inelastic coupling (Dick 2025)
4. Galactic Center Excess: E_pk = 4.60 GeV, ΔAIC = −16.3 vs PLEC
5. Lorentz invariance: null photon dispersion from Fermi-LAT GRBs
6. SVEA quantum bridge: L₂ error below 4%
7. CMB acoustic peaks without dark matter: positions within 1.5% of Planck (CLASS implementation, Ω_cdm = 0)

Falsifiable prediction: a₀(z) = (c/6)H(z) — the MOND acceleration scale evolves with redshift, testable with JWST.

Files included:

• QVR_v2.pdf — Full paper (15 pages, 5 figures, 4 tables)
• Data Set.zip — Pantheon+ SNe, SPARC rotation curves, Fermi-LAT GRB and GCE data
• QVR_Outputs.zip — All validation figures and SPARC scan results
• CLASS Scripts.zip — Patcher, runner, and λ-scan script for the CLASS Boltzmann solver
• QVR_v2_Complete_Validation_Suite.ipynb - Google Colab notebook reproducing all seven pillars