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Every signal propagating through the universe is at least weakly lensed bythe intervening gravitational field. In some situations, wave-optics phenomena(diffraction, interference) can be observed as frequency-dependent modulationsof the waveform of gravitational waves (GWs). We will denote these signaturesas Wave-Optics Features (WOFs) and analyze them in detail. Our framework canefficiently and accurately compute WOF in the single-image regime, of whichweak lensing is a limit. The phenomenology of WOF is rich and offers valuableinformation: the dense cusps of individual halos appear as peaks in Green'sfunction for lensing. If resolved, these features probe the number, effectivemasses, spatial distribution and inner profiles of substructures. Highsignal-to-noise GW signals reveal WOFs well beyond the Einstein radius, leadingto a fair probability of observation by upcoming detectors such as LISA.Potential applications of WOF include reconstruction of the lens' projecteddensity, delensing standard sirens and inferring large-scale structuremorphology and the halo mass function. Because WOF are sourced by light haloswith negligible baryonic content, their detection (or lack thereof) holdspromise to test dark matter scenarios.

Weakly Lensed Gravitational Waves: Probing Cosmic Structures with Wave-Optics Features