Ultra-low-frequency gravitational waves from cosmological and astrophysical processes

Gravitational waves at ultra-low frequencies (less than or similar to 100 nHz) are key to understanding the assembly and evolution of astrophysical black hole binaries with masses similar to 10(6)-10(9) M-circle dot at low redshifts(1-3). These gravitational waves also offer a unique window into a wide variety of cosmological processes(4-11). Pulsar timing arrays(12-14) are beginning to measure(15) this stochastic signal at similar to 1-100 nHz and the combination of data from several arrays(16-19) is expected to confirm a detection in the next few years(20). The dominant physical processes generating gravitational radiation at nHz frequencies are still uncertain. Pulsar timing array observations alone are currently unable(21) to distinguish a binary black hole astrophysical foreground(22) from a cosmological background due to, say, a first-order phase transition at a temperature similar to 1-100 MeV in a weakly interacting dark sector(8-11). This letter explores the extent to which incorporating integrated bounds on the ultra-low-frequency gravitational wave spectrum from any combination of cosmic microwave background(23,24), big bang nucleosynethesis(25,26) or astrometric(27,28) observations can help to break this degeneracy.