Constraining the gravitational-wave breathing mode with LVK antenna patterns and GWTC data

Metric theories of gravity admit a massless breathing scalar b besides the tensor modes + and times. Many scalar--tensor models predict a much smaller breathing amplitude; gravitational quantum field theory (GQFT) instead allows h b comparable to the tensor amplitudes. We evaluate the LIGO--Virgo--KAGRA (LVK) antenna patterns with PyCBC, including Michelson suppression of b. Here F b is the breathing antenna pattern and S b= sum d F b d2 is the network breathing power. At the H1 zenith at the GW150914 epoch, F b about 5 times 10-6; for 72 Gravitational-wave Transient Catalog (GWTC) events with packaged strain the median inclination gain in S b is about 34 times. Ranking multi-detector GWTC events (network SNR 8, 2 sites) by SNR sqrt S b* identifies loud O4 triggers and GW170817 as geometric targets. Parameter-estimation (PE) weighted S b on twelve events shows that the true sky can suppress this ranking (GW170817) and that GW200129 065458, GW150914, and GW190814 have the highest PE-weighted S b for ξ in h b=ξh+ (GR: ξ 0). An HLV design-noise injection grid gives B(GR+b/GR) about 13 (4) for ξ=1 (0.5) on an inclined sky (S b about 0.18); near zenith (S b about 0.016) the ξ posterior remains unconstrained. The GWTC limits are semi-joint: masses and spins fixed at PE medians, while d L, θ JN, sky, and ξ vary within PE-informed priors. Eleven of twelve events are analyzed (GW170817 omitted: PE sky on the breathing null). None favors GR+b; ξ 90% about 0.15, 0.18, and 0.23 for GW150914, GW200129 065458, and GW200311 115853 disfavor ξ about O(1), while weaker bounds (including GW190814) still allow that scale.