Gravitational wave backgrounds from colliding exotic compact objects

Long-baseline atom interferometers offer an exciting opportunity to explore midband gravitational waves with frequencies of 1 mHz-10 Hz. In this work we survey the landscape of possible contributions to the total gravitational wave background from merging binary systems in this frequency band and advocate for targeting this observable. Such an approach is complimentary to searches for resolved mergers from individual sources and may have much to reveal about the Universe. We highlight that the inspiral phases of known stellar-mass compact binaries cumulatively produce a signal well within reach of the proposed AION-km and AEDGE experiments which will need to be accounted for in the gravitational wave programs of these experiments. We further show that hypothetical populations of dark sector exotic compact objects, harboring just a tiny fraction of the dark energy density, could generate signatures unique to gravitational wave detectors sensitive to subhertz frequencies, providing a novel means to probe complexity in the dark sector.