Phase-Modulated Graviton–Higgs Coupling Tested With LIGO Strain

Abstract

This paper presents a phase-modulated local Higgs-field coupling model for possible effective graviton mass acquisition in a reduced time-domain representation. The model introduces a complex analytic envelope, obtained through the Hilbert transform of a real strain-like waveform, into a hyperbolic evolution operator with a phase factor √(−i) exp(iωt). The corresponding right-hand side is written as a reduced Klein–Gordon-like response containing a second time derivative and an effective local mass-coupling term m_eff²(t) = g_H²|Φ_H(t)|². The formulation is evaluated in two stages: first with a controlled sinusoidal waveform and then with publicly available LIGO/GWOSC strain data. In both stages, the left- and right-hand sides are compared after Z-score normalization, and the mean absolute error is used as an operational compatibility metric. The revised interpretation does not claim direct detection of massive gravitons; rather, it reports model-based consistency between the proposed phase-modulated operator and normalized gravitational-wave strain-derived behavior. The results suggest that the proposed mathematical structure is suitable for further testing with multiple gravitational-wave events, detector channels, and alternative forms of Φ_H(t).