Ultra-low frequency gravitational waves: distinguishing cosmological backgrounds from astrophysical foregrounds

The gravitational wave (GW) spectrum at frequencies below $\sim 100\,\mathrm{nHz}$ may contain overlapping contributions from processes in the early Universe and black hole binaries with masses $\sim 10^{6}-10^{9}\,M_\odot$ at low redshifts. Pulsar timing arrays are measuring the GW background at $\sim 1-100\,\mathrm{nHz}$, but are currently unable to distinguish an astrophysical foreground from a cosmological background due to, say, a first order phase transition at a temperature $\sim 1-100\,\mathrm{MeV}$ in a weakly-interacting dark sector. Our analysis reveals the extent to which including integrated bounds on the ultra-low frequency GW spectrum from cosmic microwave background, big bang nucleosynethesis or astrometric observations can break this degeneracy.