Multimessenger Tomography of Inhomogeneous Dark Matter Structure via Gravitational Wave and Electromagnetic Arrival Time Differentials

We propose a novel observational framework for probing the inhomogeneous distribution of dark matteralong cosmological lines of sight, using coincident gravitational wave (GW) and electromagnetic (EM)signals from compact binary merger events as a dual-channel propagation probe. Gravitational waves,interacting negligibly with intervening matter at leading order, serve as vacuum propagation referencesignals. Photons accumulate a small but measurable phase delay as they traverse regions of elevateddark matter density, generating an effective refractive index n > 1 in those regions. Over cosmologicalbaselines, the integrated column density of dark matter along each line of sight imprints a characteristicarrival time differential Δt between the GW and EM signals, above and beyond contributions from astrophysicalsource timing uncertainties. We show that a statistical ensemble of multimessenger events atvarying redshifts and sky positions, cross-correlated with large-scale structure maps, allows separation ofthe dark matter propagation signal from astrophysical noise. This constitutes a direct analogue of thedispersion measure technique used in pulsar timing for ionized plasma, extended to the dark sector. Theframework places constraints on dark matter models that predict nonzero photon–dark matter forwardscattering amplitudes, including millicharged dark matter, ultralight dark matter, and dark photon models.Third-generation gravitational wave detectors, including the Einstein Telescope and Cosmic Explorer,will provide the event rates necessary to make this program statistically competitive.