  The detection of gravitational waves (GWs) has opened a new window to test
the fundamental nature of gravity. We present constraints on the nonstandard
propagation of GWs using the spectral siren method applied to binary black hole
(BBH) mergers from the third Gravitational-Wave Transient Catalog (GWTC-3). The
spectral siren method exploits the redshift distribution of BBHs to probe the
cosmic expansion history and break degeneracies between cosmology and modified
gravity effects. We focus on the friction term $\nu$ in the nonstandard GW
propagation equation, which characterizes the running of the Planck mass.
Assuming the standard $\Lambda$CDM cosmology, we find $\nu = 0.5^{+3.5}_{-2.6}$
(median and $90\%$ credible interval), improving upon previous constraints from
the bright siren event GW170817 by an order of magnitude. This improvement is
due to the higher redshifts of BBHs in GWTC-3, reaching up to $z \sim 1$. Our
result suggests that the propagation of GWs is consistent with the predictions
of general relativity, placing limits on modified gravity theories that predict
a time-varying Planck mass. As the sensitivity of GW detectors improves, the
spectral siren method will provide a powerful tool for testing gravity on
cosmological scales and probing the physics of the early Universe.
