The dark timbre of gravitational waves

Gravitational wave timbre, the relative amplitude and phase of the different frequency harmonics, can change due to interactions with low-mass halos. We focus on binaries in the LISA range and find that the integrated lens effect of cold dark matter structures can be used to probe the existence of $M_{\mathrm{v}}\lesssim 10M_{\odot }$ halos if a single binary with eccentricity $e=0.3-0.6$ is detected with a signal-to-noise ratio $100-{10}^3$ and it is at $z_s=0.5$.