Action-level characterization of gravitational-wave propagation in dynamical Barbero--Immirzi gravity

Abstract

We investigate which operators in first-order dynamical Barbero--Immirzi (BI) gravity control cosmological tensor propagation at the action level. Within a bosonic, two-derivative, curvature-linear Einstein--Cartan class, eliminating the algebraic Lorentz connection reveals a separation between the scalar sector and the tensor kinetic normalization. In particular, the Holst-to-Palatini ratio determines the scalar kinetic structure, whereas the transverse-traceless tensor mode is normalized by the parity-even Hilbert--Palatini coefficient. As a consequence, a minimal dynamical Holst sector with fixed parity-even normalization remains exactly on the general-relativistic tensor-propagation surface and does not generate anomalous gravitational-wave friction. We then construct a regular nonminimal parity-even realization in which the tensor normalization evolves cosmologically, derive the corresponding standard-siren observable, and apply current GWTC-3, GWTC-4.0, and GWTC-5.0 information as an observational test of this action-level tensor sector. The resulting constraints should therefore be interpreted as limits on the evolution of the tensor kinetic normalization rather than direct constraints on minimal BI torsion dynamics.

15 pages, 5 figures. Revised version