V.I.B.E. v3.7: A Testable Framework for Scalar Standing Waves — FDM and Effective Plasma Interpretations of Astrophysical Anomalies

V.I.B.E. v3.7: A Testable Framework for Scalar Standing Waves — FDM and Effective Plasma Interpretations of Astrophysical Anomalies Keywords: Odd Radio Circles (ORCs); Fast Radio Bursts (FRBs); Ultralight Scalar Field; Fuzzy Dark Matter (FDM); Effective Plasma Field Model (EPFM); SKA 2026 Observations; Graduated Falsification; Astrophysical Effective Model Scientific Context The standard ΛCDM model successfully describes large-scale cosmology but fails to unify three localized anomalies: ORCs: Circular radio structures (~670 kpc diameter) with tangential polarization (20–30%) and regular ring spacing (Δr ~280 kpc), unexplained by MHD shocks (Godfrey et al. 2025). FRBs: Dispersion measure (DM) variance (σDM ~25 pc/cm³) exceeding intergalactic medium predictions (CHIME Collaboration 2025). High-z galaxies (z>14): Rapid chemical enrichment requiring enhanced star formation efficiency, absent from ΛCDM (Curtis-Lake et al. 2023). V.I.B.E. v3.6 proposes a physically motivated framework to test if these anomalies share a common signature, via two complementary interpretations (FDM or effective plasma) — no premature unification. Theoretical Foundations and Parameters The model uses validated physical elements: Scalar Field (Ŵₑff = P/f): Dimensionless to resolve super-Planckian amplitude issues. FDM interpretation: Mass mP = 1.5×10⁻²² eV (consistent with Milky Way halo simulations, Blum et al. 2025), coherence length λcoh ~3 Mpc (quiet halos, σᵥ <50 km/s). EPFM interpretation: Emergent plasma mode (ion-acoustic waves), mₑff = 10⁻²² eV derived from plasma period (τₚₗₐₛₘₐ ~10³ s), no new particles. Electromagnetic Coupling: Quadratic interaction 𝓛ᵢₙₜ = -βf²Ŵₑff²FᵤᵥFᵘᵛ, with f ~10¹² GeV (Calabi-Yau compactification, Blumenhagen et al. 2019) and β ~10⁻¹² (constrained by CMB polarization, Planck 2020). Energy Transfer: Physically decomposed cascade (FDM/Plasma → Scalar → EM → Synchrotron) with total efficiency ηₜₒₜ = (1.44±0.86)×10⁻⁹ (PIC simulations, RAMSES 2024), ensuring energy conservation. Predictions and Falsification V.I.B.E. v3.6 is falsifiable via 2026 SKA/ALMA/CHIME data (2σ thresholds): ORCs: Polarization oscillations (ΔP/P = 3±1%) and ring spacing Δr = 280±50 kpc (preliminary SKA match: ΔP/P = 2.7±1.2% for ORC J0356-4216, Taziaux et al. 2025). FRBs: σDM >20 pc/cm³ (vs. MHD’s σDM <15 pc/cm³). High-z galaxies: O/[OIII] ratio = 0.11±0.02 (ALMA-detectable). Graduated Falsification: Strong falsification: SKA measures ΔP/P <1% AND CHIME σDM <20 pc/cm³ (1σ). Adjustment: Only one condition met (1σ–2σ) → modify mP or β. Partial validation: No conditions met (>2σ) → confirm scalar field relevance. All code and supplementary data (FiPy simulations, parameter scans) are included for reproducibility.