  Long baseline atom interferometers offer an exciting opportunity to explore
mid-frequency gravitational waves. In this work we survey the landscape of
possible contributions to the total 'gravitational wave background' 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 find that the inspiral phases of
stellar-mass compact binaries cumulatively produce a signal well within reach
of the proposed AION-km and AEDGE experiments. Hypothetical populations of dark
sector exotic compact objects, harbouring just a tiny fraction of the dark
energy density, could also generate signatures unique to mid- and low-frequency
gravitational wave detectors, providing a novel means to probe complexity in
the dark sector.
