A gaussian-process reconstruction of gravitational-wave friction from dark standard sirens

Abstract

Standard sirens provide a direct probe of the cosmic distance-redshift relation and therefore a powerful test of whether gravitational waves (GWs) propagate as predicted by general relativity on cosmological scales. In many extensions of general relativity, GW propagation is modified by an anomalous friction term, which alters the amplitude evolution and leads to a GW luminosity distance that differs from its electromagnetic counterpart. In this work, we develop a non-parametric reconstruction of this anomalous friction from dark standard sirens. We reconstruct its redshift dependence, encoded in the friction function $α_M(z)$, with a Gaussian process (GP) and derive the corresponding GW-to-EM luminosity-distance ratio $Ξ(z)$ by integration, explicitly retaining the relation between the local friction modification and its accumulated effect on the observed distance, while enforcing a monotonic and invertible GW luminosity distance. We apply the method to the GWTC-5.0 catalog, jointly inferring the source population, modified propagation, and background cosmological parameters. We find no evidence for departures from GR, with $α_M=0$ and $Ξ=1$ consistent with the posterior over the redshift range probed by the catalog. The result is stable under variations of the GP kernel, smoothness and amplitude priors, resolution prescription, and likelihood treatment. We further introduce function-space diagnostics for comparing flexible and parametric reconstructions, including prior calibration, prior-to-posterior contraction, common summaries of propagation-population degeneracies, and principal-component analysis. These tools make explicit which features are informed by the data and which are imposed by the function-space prior, providing a framework for interpretable non-parametric tests of gravitational-wave propagation.