Tidal Love Numbers in Trace-Gradient Modified Gravity: Bulk Source Dominance and Gravitational Wave Constraints

This work derives the tidal Love number equation in Trace-Gradient Modified Gravity (TGMG), a scalar-coupled extension of General Relativity parameterized by a dimensionless coupling constant β. We show that the standard interface-only approximation for neutron-star tidal deformability fails in TGMG because bulk trace-gradient sources enter the tidal perturbation equation at the same formal order as interface terms. Using the validated RG(SLy4) CompOSE equation of state, we find that 67.4% of the weighted bulk source integral originates in the stellar core, demonstrating genuine bulk dominance. An exact nonlinear Riccati formulation of the tidal problem is derived and solved without perturbative expansion. Applying the model to GW170817 yields an astrophysical upper bound β < 24.91 (90% credible level) within the stellar-sector TGMG framework. This version is released as a research preprint for public discussion and independent review.