Vibrational Fragmentation Theory of the Gravitonium and Unified Origin of Λ and ULDM

# VGF Origin and Evolution: Primordial to Post-BBN Signatures **Author:** DM.K08 **Date:** August 9, 2025 **Version:** Extended with August 9, 2025 Observations --- ## AbstractThis repository presents the study of the **Vibrational Gravitonium Fragmentation (VGF)** model, from primordial cosmological conditions to post-BBN astrophysical regimes. The framework predicts a **high-frequency gravitational wave (HFGW)** peak at MHz frequencies, modeled with a log-normal spectral profile and constrained by early-universe cosmology. Results are compared with sensitivity curves from PTA, LISA, LIGO/Virgo/KAGRA, and prospective MHz–GHz HFGW detectors. Key findings:- Consistency with **current GW bounds** across all tested bands.- Evidence of **fractal-like spectral repetition** between MHz and GHz peaks.- Strong motivation for **dedicated HFGW instrumentation**. --- ## Parameter Setup- **Primordial amplitude:** Ωp = 1×10⁻⁶ - **Parameter scan:** - k ∈ [10⁻³, 10³] Mpc⁻¹ (comoving wavenumber) - β ∈ [0, 4] (spectral index) - **Target frequency bands:** - PTA: 10⁻⁹ – 10⁻⁷ Hz - LISA: 10⁻⁴ – 10⁻¹ Hz - LIGO/Virgo/KAGRA: 10¹ – 10³ Hz - VGF peak: 10⁶ Hz --- ## Spectral ModelGravitational-wave spectrum:\[\Omega_{gw}(f) = \Omega_p \exp \left[ - \frac{\ln^2(f/f_p)}{2\sigma^2} \right]\]- **Primordial:** fp = 1 MHz, σ = 0.5, Ωp = 10⁻⁶ - **Post-BBN:** same fp and σ, but Ωp up to 10⁻⁴ --- ## Results ### Peak Amplitudes vs Observational Limits| Band | Obs. Limit | Primordial Ωgw | Post-BBN Ωgw | Status ||--------|-----------|----------------|--------------|-----------------------------|| PTA | <1×10⁻⁹ | 3×10⁻¹² | 1×10⁻¹¹ | Admitted || LISA | <1×10⁻¹¹ | 8×10⁻¹⁴ | 4×10⁻¹³ | Admitted || LIGO O4| <1×10⁻⁸ | 2×10⁻¹⁰ | 1×10⁻⁹ | Admitted || HFGW | n.a. | 1×10⁻⁶ | 1×10⁻⁴ | Requires dedicated detection | --- ### Fractal ScalingScaling from MHz to GHz peak: \[f' = 10^3 f, \quad \Omega'_{gw} = 10^3 \Omega_{gw}\] Correlation between scaled spectra: **0.9987** (near-perfect self-similarity). --- ## August 9, 2025 ObservationCERN reported a **near-threshold tt̄ excess** consistent with a quasi-bound toponium state. - Treated as a **VGF post-diction** stress-test. - No claim of confirmation — potential effects at the 10⁻³–10⁻² level remain below current sensitivity. --- ## Conclusions- **Fully admitted** by current PTA/LISA/LIGO bounds.- MHz HFGW peak is the **primary actionable target**.- Fractal spectral repetition supports testability at GHz frequencies with future detectors.- CERN event offers a **separate high-energy probe**, currently inconclusive. --- ## Repository Contents- `VFG_origin_r:evolution.pdf` → Full paper (this document) - `figures/` → Spectrum plots, admitted/excluded maps, scaling visualizations - `data/` → Numerical results from k–β scan - `scripts/` → Spectral model simulation scripts (Python/Matlab) --