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

Gravitational waves at ultra-low frequencies (≲100 nHz) are key to understanding the assembly and evolution of astrophysical black hole binaries with masses ~106–109 M⊙ at low redshifts1–3. These gravitational waves also offer a unique window into a wide variety of cosmological processes4–11. Pulsar timing arrays12–14 are beginning to measure15 this stochastic signal at ~1–100 nHz and the combination of data from several arrays16–19 is expected to confirm a detection in the next few years20. The dominant physical processes generating gravitational radiation at nHz frequencies are still uncertain. Pulsar timing array observations alone are currently unable21 to distinguish a binary black hole astrophysical foreground22 from a cosmological background due to, say, a first-order phase transition at a temperature ~1–100 MeV in a weakly interacting dark sector8–11. This letter explores the extent to which incorporating integrated bounds on the ultra-low-frequency gravitational wave spectrum from any combination of cosmic microwave background23,24, big bang nucleosynethesis25,26 or astrometric27,28 observations can help to break this degeneracy. While pulsar timing observations are currently unable to distinguish a binary black hole astrophysical foreground from a cosmological background, integrated bounds on the ultra-low-frequency gravitational wave spectrum from other cosmological probes may help to break this degeneracy.