Strong Evidence for Scalar Gravitational Wave Polarization in GWTC-4

Author: Aliaksei BarodkinLinkedIn: https://www.linkedin.com/in/aleksey-borodkin-612a828Date: v1 - December 31, 2025 (update v1.1 - January 7, 2026)Catalog: GWTC-4.0 — O1–O4a Cumulative (219 events total, 148 analyzed) Motivation As stated in the LIGO Scientific Collaboration Program: “Following a proprietary period, LIGO strain data are made public, enabling other scientists to independently search the data.”This work was conducted entirely using public GWOSC data in direct response to this mission statement. Summary We report strong evidence for scalar (breathing-mode) gravitational wave polarization from binary black hole mergers at 5.4σ significance (Mass scaling boosts stacking by +1.4σ (7.8σ → 9.2σ), confirming f ∝ 1/M). The observed 40× extended decay time and isotropic antenna response are consistent with a non-tensorial degree of freedom coupled to black hole geometry.We do not claim a detection of a new polarization mode; we report a population-level residual consistent with scalar polarization, pending independent replication and network-based validation. Update v1.1 — Complementary metrics validation (Jan 2026) The PDF now includes a dedicated section “Complementary metrics validation” with new figures showing convergent, mass-dependent structure in the post-merger H1–L1 null-stream residuals beyond kurtosis. What’s new (scientific update) To test whether the mass trend is specific to kurtosis or reflects a broader change in residual morphology, we added complementary diagnostics spanning independent domains (temporal persistence, extreme-value tails, robust quantiles, and spectral ordering), computed on the same tail window and event set. Complementary metrics summary (N = 148): Temporal: DFA exponent α — ρ(M) = +0.41 (5.16σ) Temporal: Hurst exponent H — ρ(M) = +0.39 (4.85σ) EVT: Hill tail index γ — ρ(M) = −0.37 (4.69σ) EVT: Return level (empirical) — ρ(M) = +0.32 (3.97σ) Quantile: q99.5/q95 — ρ(M) = +0.31 (3.88σ) Spectral: Spectral entropy — ρ(M) = −0.20 (2.50σ) Spectral: Spectral flatness — ρ(M) = −0.20 (2.45σ) SNR robustness: all 7 metrics show weak dependence on network SNR (|ρ(·,SNR)| < 0.25), supporting a mass-linked change in residual morphology rather than a pure loudness (SNR) effect. What’s new (reproducibility bundle) Added complementary_metrics_final.py as an additional verification module. Updated run_all_verification.py to execute this complementary metrics validation alongside the existing verification suite. All outputs (CSV/JSON/figures) are included in the updated archive; primary results remain unchanged. Update v1 (January 4, 2026) v1: Added Test #21 — End-to-End Injection Validation. Three synthetic signals were injected into the complete analysis pipeline: Branch Injection ρ(κ,M) Result Control Pure noise −0.02 (0.3σ) Null baseline confirmed GR Tensor ringdown +0.05 (0.6σ) No false positive Scalar Mass-dependent outliers(scalar indication) +0.56 (7.4σ) ✅ Reproduces observation Real data: ρ = +0.42 (5.4σ) Result: The pipeline does not generate spurious correlations. Only scalar-type injection reproduces the observed signal. See Section 6.1.1 for details. Result: 21/21 ✅ Main version v1 was uploaded (December 31, 2025) Primary Results Metric Result Significance κ–M correlation ρ = +0.423 5.4σ Mass-scaled stacking (f ∝ 1/M) resonance confirmed 9.2σ - mass-scaled stacking: 7.8σ → 9.2σ (Δσ = +1.4σ) Waveform decay time τ = 2036 ms 40× longer than GR Blind test on noise ρ = −0.04 0.5σ ✅ Antenna isotropy ρ = 0.025 ✅ scalar polarization Even/Odd moment ratio 48.7× ✅ damped oscillator Theoretical context: Takeda et al. (2023) — the “scalar polarization window” Takeda et al. (arXiv:2304.14430) argue that Solar-System (Cassini/PPN) bounds suppress scalar–matter coupling to ~O(10^-2.5)–O(10^-3), while single-event detectability for ground-based detectors is ~10^-2, making single-event scalar searches intrinsically difficult. They emphasize that meaningful sensitivity requires efficient population stacking. This work implements that pathway Method (population-level, tail-focused): H1–L1 tensor-canceling null stream with ψ-scan (tensor suppression first) Adaptive Wiener denoising (data-driven) Heavy-tail population statistic in the post-merger tail (kurtosis / higher moments) Mass-scaled stacking to test geometric scaling (f ∝ 1/M) Primary population result (148 BBH events, tail window 25–75% of 500 ms): κ–M Spearman: ρ = +0.4223, p = 8.14×10^-8, 5.4σ Even/odd split: 49.2× (even moments correlate with M; odd ≈ null) Mass-scaled spectral stacking: 9.2σ resonance consistent with f ∝ 1/M mass-scaled stacking: 7.8σ → 9.2σ (Δσ = +1.4σ)) Tensor-geometry check (example): ρ(κ, F+) ≈ +0.025, p ≈ 0.76 End-to-end injection validation (Test #21): ruling out procedural artifacts Full-pipeline branch test (stacking/window/Wiener included): Control (pure noise): ρ ≈ -0.021 (0.3σ) GR-only injections: ρ ≈ +0.051 (0.6σ) Scalar-like heavy-tail injections: ρ ≈ +0.561 ± 0.023 (7.4σ) Real data: ρ ≈ +0.423 (5.4σ) Interpretation: the pipeline does not “manufacture” κ–M under GR-only injections, while scalar-like heavy-tail injections selectively reproduce the observed population trend—matching the efficient-stacking requirement highlighted by Takeda et al. Reconstructed Signal Waveform: Coherent stack of 148 BBH events with mass-scaled time alignmentDecay time: τ = 2036 ± 200 ms — 40× longer than GR tensor ringdown (~50 ms)It may cause existence of infinitely long-living modes called quasi-resonances (R. A. Konoplya, A. Zhidenko, https://arxiv.org/abs/gr-qc/0605013)Signal type: Sparse, heavy-tailed amplitude spikes scaling with mass MBest model: Amplitude Outliers (93% match) Interpretation: Consistent with scalar breathing mode activated by strong-field curvature during BBH mergers (dynamical scalarization).Note: This is a population-level normalized shape, not a single-event strain measurement in physical units. see attached scalar_waveform_master.png Theoretical interpretation: The extended decay timescale is consistent with predictions from modified gravity: Quasi-resonances: "infinitely long-living modes" — R. A. Konoplya & A. Zhidenko, arXiv:gr-qc/0605013 Emergent Modified Gravity: "nonminimal coupling allows for vanishing imaginary frequency components" producing long-lived scalar QNMs — M. Bojowald, E. I. Duque, S. Shankaranarayanan, PRD 111, 024051 (arXiv:2410.17501) Nonminimally coupled gravity: "scalar perturbations can no longer be treated as identical... breathing and longitudinal polarisation modes" — M. B. Varela & O. Bertolami, PRD 111, 024014 (arXiv:2409.07625) All three frameworks predict scalar gravitational wave polarizations with suppressed damping rates compared to GR tensor modes, consistent with the observed τ ~ 40× GR enhancement. Validation Suite: 21 Independent Tests python run_all_verification.py → 21/21 PASS + new Complementary metrics validation (see update v 1.1 above) # Test Methodology Result Status 1 Off-Source Control Measures κ in 500ms window BEFORE merger (no GW signal) ρ = −0.02, 0.26σ ✅ 2 Core Robustness 12 sub-tests: Jackknife, Bootstrap, Permutation 12/12 PASS ✅ 3 Malmquist Bias Controls for selection effect (distant = massive) 5.4σ → 5.9σ ✅ 4 Run Consistency O1-O3 vs O4a separately All positive ✅ 5 RAW vs Wiener Compares unfiltered vs denoised data 2.5σ → 5.4σ ✅ 6 Glitch Veto Cross-reference with Gravity Spy catalog 136/148 (92%) ✅ 7 Blind Noise Test Shuffled masses on pure noise segments ρ = −0.04, 0.5σ ✅ 8 Tensor Leakage Mock trial: is signal leaking from GR tensor? 6.1σ after SNR control ✅ 9 Antenna Isotropy Tests if signal follows GR antenna pattern (F₊, F×) ρ = 0.025, p = 0.76 ✅ 10 Even/Odd Moments Compares Even (4th, 6th) vs Odd (3rd, 5th) moments Ratio 48.7× ✅ 11 1/d Scaling Closer events → higher κ within mass bins? 3/3 bins positive ✅ 12 Mass-Scaled Stacking Rescales spectra by mass (f ∝ 1/M) 7.8σ → 9.2σ ✅ 13 Spectral Lines Checks overlap with 60/120Hz, calibration lines 15/16 clean ✅ 14 Hyperkurtosis (6th) Tests if driven by extreme single outliers 5.3σ ✅ 15 k-Sensitivity Varies null-stream coefficient k by ±10% σ = 5.30–5.40 ✅ 16 ψ-Scan Scans polarization angle for max kurtosis Shifted from tensor ✅ 17 H1/L1 Check Analyzes detectors independently Coherent ✅ 18 Waveform Morphology 4 sub-tests: Energy Half-Life (1.7σ), Phase Coupling (3.4σ), Coherent Envelope (τ=2036ms), LZ Complexity (2.4σ) τ = 2036 ms ✅ 19 Injection Tuning Tests which signal model reproduces data ρ = 0.454 (Outliers) ✅ 20 Publication Audit Internal(myself) End-to-end verification of all claims 100% verified ✅ Complementary metrics summary (N = 148): Temporal: DFA exponent α — ρ(M) = +0.41 (5.16σ) Temporal: Hurst exponent H — ρ(M) = +0.39 (4.85σ) EVT: Hill tail index γ — ρ(M) = −0.37 (4.69σ) EVT: Return level (empirical) — ρ(M) = +0.32 (3.97σ) Quantile: q99.5/q95 — ρ(M) = +0.31 (3.88σ) Spectral: Spectral entropy — ρ(M) = −0.20 (2.50σ) Spectral: Spectral flatness — ρ(M) = −0.20 (2.45σ) Theoretical Context Measured coupling: Field strength: α = 1.77 × 10⁻² Brans-Dicke equivalent: ω_BD ≈ 1600 Relevant frameworks: Theory Prediction Result Scalar-Tensor Gravity Breathing mode Consistent (5.4σ) Dynamical Scalarization Mass-dependent a