Ultra-low frequency gravitational waves from cosmological and astrophysical processes

Gravitational waves (GWs) at ultra-low frequencies (${\lesssim 100\,\mathrm{nHz}}$) are key to understanding the assembly and evolution of astrophysical black hole (BH) binaries with masses $\sim 10^{6}-10^{9}\,M_\odot$ at low redshifts. These GWs also offer a unique window into a wide variety of cosmological processes. Pulsar timing arrays (PTAs) are beginning to measure this stochastic signal at $\sim 1-100\,\mathrm{nHz}$ and the combination of data from several arrays is expected to confirm a detection in the next few years. The dominant physical processes generating gravitational radiation at $\mathrm{nHz}$ frequencies are still uncertain. PTA observations alone are currently unable to distinguish a binary BH 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. This letter explores the extent to which incorporating integrated bounds on the ultra-low frequency GW spectrum from any combination of cosmic microwave background, big bang nucleosynethesis or astrometric observations can help to break this degeneracy.