Strong Evidence for Scalar Gravitational Wave Polarization in the complete GWTC-4(O1–O4a) catalog

Author: Aliaksei BarodkinLinkedIn: https://www.linkedin.com/in/aleksey-borodkin-612a828Date: v1 - December 31, 2025updates: (update v1.1 - January 7, 2026, v1.2 - January 12, 2026, v.1.3 - January 25, 2026)Catalog: GWTC-4.0 — O1–O4a Cumulative (219 events total, 149 analyzed) Acknowledgments I would like to express my deepest gratitude to Dr. Sourav Roy Chowdhury (PhD) for his invaluable advice, profound insights, and exceptional guidance throughout the preparation and validation of versions 1.1 – 1.3 of this work 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. 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) Blind test on noise ρ = −0.04 0.5σ ✅ Antenna isotropy ρ = 0.025 ✅ scalar polarization Even/Odd moment ratio 48.7× ✅ damped oscillator v1.3 update (current), Robustness against optimization and instrument-response artifacts This update adds robustness / negative-control tests addressing two recurring concerns:(i) optimization artifacts (e.g., narrowband lines, single-frequency ψ choices, higher-mode localized structure), and(ii) instrument-response systematics (frequency-dependent antenna response / long-wavelength approximation limits / beyond-eikonal optics). The analysis remains an independent, population-level study of post-merger H1–L1 null-stream residual morphology in GWTC‑4 BBH events, with full code + artifacts released for replication. Literature incorporated (methodological context) These robustness extensions are motivated by community methodological feedback and are aligned with ideas discussed in: Arkadiusz Błaut (2015) — Laser interferometer response to scalar massive gravitational waves, Phys. Rev. D 92, 063013. Pratyusava Baral et al. (2025) — Parameter estimation of gravitational-wave signals with frequency-dependent antenna responses and higher modes, Class. Quantum Grav. 42, 215007. Andrea Virtuoso & Edoardo Milotti (2025) — Beyond the long wavelength approximation: Next-generation gravitational-wave detectors and frequency-dependent antenna patterns, Phys. Rev. D 111, 064058. Thomas B. Mieling (2021) — The response of laser interferometric gravitational wave detectors beyond the eikonal equation, Class. Quantum Grav. 38, 175007. 1) Frequency-binned polarization optimization (anti–narrowband artifact test) To test whether the population trend could be driven by single-frequency ψ optimization (e.g., narrowband spectral lines, localized glitch features, or higher-mode content concentrated in a limited region), we repeat the full analysis with frequency-binned null-energy minimization (conceptually aligned with frequency-dependent response / likelihood ideas discussed in Baral et al. (2025)). Instead of optimizing ψ at a single effective frequency, we minimize null-stream residual energy across three physical bands: 60–120 Hz 120–200 Hz 200–350 Hz All downstream steps are unchanged (windowing, Wiener denoising, tail statistics, population tests). Result (N = 149 BBH): ρₛₚₑₐᵣₘₐₙ(κ, M): 0.422 → 0.411 significance: 5.36σ → 5.20σ per-event κ agreement between pipelines: r = 0.998 Interpretation: the effect is not driven by single-frequency ψ-optimization artifacts; it reflects broad-band post-merger residual structure. 2) Long-wavelength approximation / frequency-dependent response sanity check Because null-stream construction depends on antenna response ratios, we test whether modest frequency-dependent response effects could bias ψ optimization or inflate heavy-tail diagnostics. We evaluate a conservative arm-length suppression factor: F(f) ∝ sinc(π f L / c), with LIGO arm length L = 4 km This sanity check is motivated by frequency-dependent antenna-pattern discussions beyond LWA (e.g., Virtuoso & Milotti (2025)). Over 60–350 Hz: implied response correction: ≤ 10⁻³ across the catalog maximum correction: 10⁻⁵–10⁻⁴ (depending on f₍dom₎ proxy) changes in σ_on: sub-percent κ–M trend: stable Interpretation: LWA remains valid for the present analysis band; modest frequency-dependent corrections cannot explain the observed population trend. 3) Beyond-eikonal / instrumental bounds (negative control) As a conservative negative control, we estimate order-of-magnitude bounds from beyond-eikonal optical response considerations (used only as a sanity bound, not subtraction). This is motivated by Mieling (2021). Result: the observed merger-localized heavy-tail residual morphology exceeds conservative instrumental bounds by orders of magnitude across the catalog. Combined with off-source null tests (no analogous mass trend), this disfavors known response-level artifacts as the dominant explanation. 4) Model-agnostic mass-rescaling diagnostic: differential gain → fine α-scan + shuffle test Step A: Differential gain test (find the target frequency) We first run an independent “differential gain” procedure that searches for the frequency where mass-scaling produces a positive focusing gain: stationary noise should smear under incorrect scaling (Gain ≤ 0) a real population feature with mass-linked frequency should focus (Gain > 0) This scan identifies the maximum-gain frequency: f₀ = 134.3 Hz Why 134.3 Hz? 134.3 Hz is not tuned in the α-scan.It is chosen from the independent differential-gain step above, and then treated as a fixed target in the fine α-scan. This reduces “look-elsewhere” freedom inside the α-scan itself. Step B: Fine α-scan at fixed f₀ = 134.3 Hz (±5 Hz) We then scan the mass-rescaling exponent α in frequency-domain stacking (evaluated near 134.3 Hz ± 5 Hz): best α*: 0.55 (peak gain +2.183 dB) ≥90%-of-peak plateau: α ∈ [0.50, 0.80](diagnostic stability range; not a frequentist confidence interval) Permutation (mass-shuffle) test at α:* 0/1000 mass-shuffles ≥ physical gain p ≈ 10⁻³, ≈ 3.09σ Interpretation: the stacked spectral coherence is genuinely mass-linked and difficult to reproduce with stationary (mass-independent) structure. 5) Low-mass control sample (negative control) As an additional negative control, we examine low-mass BBH systems where no extended post-merger structure is expected. Representative low-mass events: GW170608 (18.4 M☉): κ = +0.16 GW190725 (18.1 M☉): κ = +0.29 GW190924 (13.9 M☉): κ = −0.19 GW230627 (14.2 M☉): κ = −0.04 All four are consistent with κ ≈ 0 (noise-dominated). Population summary: low-mass subset M < 25 M☉ (N = 30): ⟨κ⟩ = −0.05 high-mass subset M > 60 M☉ (N = 74): ⟨κ⟩ = +0.50 Interpretation: an order-of-magnitude contrast supports a genuinely mass-dependent population effect rather than a uniform pipeline systematic. Additional files included in v1.3 - find them in source_code_ligo_scalar_strong_evidence_5_sigma.zip gwtc4_scalar_analysis_freq_binned.pyv1.3 robustness pipeline implementing:(i) frequency-binned ψ optimization across {60–120, 120–200, 200–350} Hz (Baral 2025 context),(ii) conservative LWA / frequency-response sanity checks (Virtuoso & Milotti 2025 context), and(iii) a beyond-eikonal instrumental sanity bound (Mieling 2021 context).All downstream steps are unchanged (windowing, Wiener denoising, tail-statistics, population tests). scaling_sanity_check.pyDifferential gain scan that finds the target frequency f₀ = 134.3 Hz by locating where mass-scaling yields positive focusing gain, and performs a mass-shuffle test at that frequency. alpha_fine_scan_fixed.pyFine α-scan at fixed target frequency f₀ = 134.3 Hz (±5 Hz), plus 1000× mass-permutation (shuffle) test. complementary_metrics_with_lowmass.pyApplies the same tail-statistics and complementary diagnostics to a dedicated low-mass control subset (M < 25 M☉). Bottom line (v1.3) New corresponding sections were added to PDF v1.3: 4.6 Frequency-binned polarization optimization (v1.3 robustnesstest) 4.7 Long-wavelength approximation and frequency-dependent re-sponse (sanity validation) 4.8 Beyond-eikonal / instrumental response bounds (negativecontrol) 4.9 Model-agnostic mass-scaling diagnostic: fine α-scan and shuf-fle test 4.10 Low-mass control sample (negative test) After frequency-binned ψ optimization, conservative LWA/frequency-response sanity checks, beyond-eikonal instrumental bounds, differential-gain targeting + fine α-scan with shuffle controls, and an explicit low-mass negative control, the population-level signal remains: significant (~5.2σ) merger-localized robust to methodological variations inconsistent with uniform detector/pipeline artifacts Update v1.2 (Jan 2026) — Off-source null validation + fixed-ψ control + Wiener preservation closure This release extends the PDF with additional systematic closure tests: (1) Off-source null validation (Complementary metrics).The complementary diagnostics (temporal persistence, EVT tails, robust quantiles, spectral ordering) are repeated on off-source windows. All 7 metrics show no statis