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 redshifts^1,2,3. These gravitational waves also offer a unique window into a wide variety of cosmological processes^{4,5,6,7,8,9,10,11.} Pulsar timing arrays^12,13,14 are beginning to measure¹⁵ this stochastic signal at ~1–100 nHz and the combination of data from several arrays^16,17,18,19 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 sector^8,9,10,11. 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.