Integrated cosmological memory: A dark-siren method to probe dark energy

Abstract

Gravitational-wave (GW) cosmology is currently bottlenecked by the scarcity of electromagnetic counterparts for bright sirens and the systematic uncertainties of galaxy catalogs for dark sirens. We propose a purely gravitational resolution using the Integrated Cosmological Memory (ICM)-the cumulative GW strain encoded in the spacetime geometry of an expanding Universe. While the GW transient emitted by the source provides the luminosity distance, the ICM accumulates a mathematically distinct integral of the cosmic expansion history. We demonstrate that extracting both observables from a single binary merger completely breaks the distance-redshift degeneracy within the gravitational sector. This establishes a novel, catalog-free dark siren framework for third-generation GW detector networks. Crucially, the resulting constraints on late-time dark energy are only weakly sensitive to the local expansion rate, providing a robust cosmological probe that can potentially mitigate the impact of the H0 tension.