Gravitational-wave propagation constraints on the dynamical Barbero--Immirzi field from GWTC-3 dark sirens

Abstract

The Barbero--Immirzi (BI) parameter, originally a constant in the Holst term of first-order gravity, can be promoted to a dynamical scalar field $\gamma(x)$ coupled to torsion in Einstein--Cartan theory. We formulate the leading gravitational-wave (GW) propagation effect of this dynamical BI sector as an effective friction term, $\Gamma_{\rm BI}=\xi_{\rm BI}H$, and relate it to the GW luminosity distance. We then compare the resulting distance-redshift relation with the published LIGO--Virgo--KAGRA GWTC-3 dark-siren constraint on the Belgacem--Maggiore parameter $\Xi_{0}=1.2^{+0.7}_{-0.7}$. Without repeating the LVK hierarchical Bayesian analysis, and using a representative-redshift mapping together with a Gaussian approximation to the quoted posterior, we obtain the conservative effective constraint $|\xi_{\rm BI}|\lesssim 2.1$ at approximately 90\% credibility. For the specific BI realization considered here, $\xi_{\rm BI}$ is non-negative at the leading order adopted, so the corresponding one-sided interpretation is $0\leq\xi_{\rm BI}\lesssim 2.1$. The observable constraint is therefore a statement about the effective BI-induced GW friction. Translating it into the microscopic fluctuation amplitude requires an independent normalization of the BI--torsion sector; we do not impose such a normalization phenomenologically. This GW-propagation test probes a sector complementary to torsion-wave and matter-sector constraints and does not rely on an assumption that astrophysical sources excite propagating torsion modes.