A Palatini PT-Even Torsion Framework: Conditional Uniqueness, Bulk Rank-One Equivalences, and Tensor Luminality via Coefficient Locking
Chien-Chih Chen · Preprints.org · 2025
We present a symmetry-based framework for torsionful gravity in the Palatini formulation that ensures luminal gravitational waves (c_T = 1) without parameter tuning and without extra propagating modes. The organizing principle is a scalar PT projector on observable scalar densities, paired with projective symmetry implemented by a Stueckelberg compensator epsilon(x) that enters only through the invariant trace T_mu − partial_mu epsilon. Within a two-derivative, parity-even posture (A1–A5) we establish three conditional results: (C1) pure-trace alignment, fixing torsion by partial_mu epsilon while axial and traceless irreps vanish; (C2) three-route bulk equivalence, showing that determinant/rank-one, closed-metric, and PT-even CS+ constructions share the same quadratic bulk up to improvement currents; and (C3) coefficient locking, which removes TT–non-TT mixing and enforces K = G, hence c_T = 1 exactly at quadratic order with only two tensor degrees of freedom. The leading parity-even NLO correction is unique and predicts delta c_T^2(k) = b k^2 / Lambda^2 for k 0) in the strict spurion limit. A projectively invariant Stueckelberg completion with m_T -> infinity (or a Lagrange current enforcing T_mu − partial_mu epsilon) explains the gradient-only appearance of epsilon and justifies treating it as nondynamical at low energies; residual dynamics would yield controlled, testable deviations. All figures and reductions are reproducible from a public code release. The framework delineates a symmetry-selected, data-facing sector of torsionful modified gravity consistent with multimessenger bounds.