Galactic and extragalactic probe of dark matter with LISA's binary black holes

Abstract The upcoming LISA mission will be able to detect gravitational waves from galactic and extragalactic compact binaries. Here, we report on LISA's capability to probe dark matter around these binaries if the latter constitute black holes. By analyzing the variation in the chirp mass of the binary, we show that depending on the black hole masses, LISA should be able to probe their surrounding dark matter to a luminosity distance of ≈ 1 Gpc if such binaries are located within the inner ≈ 10 pc of their galactic center for particle-like dark matter or near the galactic solitonic core for wave-like dark matter. However, for the latter, the density of dark matter near the galactic center must be higher than predicted from dark matter only simulations. Even if a null result is recorded during the course of observation of well-localized binaries, one can rule out certain parameter spaces of dark matter as being the dominant contributor to the matter budget of the Universe.