Propagating Axial Torsion and Gravitational‐Wave Amplitude in Dynamical Barbero–Immirzi Gravity: Implications for GWTC ‐3

We revisit gravitational‐wave (GW) propagation with a dynamical Barbero–Immirzi (BI) field and a genuinely propagating axial‐torsion mode. We define a restricted metric‐compatible first‐order Einstein–Cartan–Holst parent with a Maxwell‐type axial kinetic term, explicitly decompose its parity‐even and Holst curvature invariants into torsion irreducible components, and give an explicit prescription for the restricted bare‐coupling family that realises an exact scalar–Proca reduction. On a regular branch, the nonlinear reduced theory propagates two tensor, one scalar and three massive vector modes. A constraint count, a positive local Proca Hamiltonian and a healthy Minkowski spectrum verify the regular branch under explicit sign conditions. Independent component‐level checks test both the curvature–torsion quadratic coefficients and their divergence terms. On an isotropic background with vanishing shifted‐vector condensate, the tensor kinetic and gradient coefficients both equal : and the additional friction is , which originates from this independently specified parity‐even coupling, not from the torsion pole itself. The resulting geometric‐optics luminosity‐distance ratio is and equals unity at zero redshift. We exhibit a rolling BI solution satisfying the vacuum background equations, but do not regard it as a fit to GWTC‐3. Published phenomenological propagation constraints cannot by themselves furnish a BI parameter limit. The constructed first‐order parent is restricted and does not establish stability for arbitrary Poincaré gauge operators.