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.

引力波在超低频率（≲ 100 NHZ）是了解该组件，并用质量〜10的天体物理学黑洞二进制进化⁶ -10 ⁹ 中号_⊙在低红移^1,2,3。这些引力波还为了解各种宇宙学过程提供了一个独特的窗口^{4,5,6,7,8,9,10,11}。脉冲星定时阵列^12、13、14开始测量¹⁵这种随机信号，频率约为 1-100 nHz，来自多个阵列^{16、17、18、19}的数据的组合预计将在未来几年内确认检测²⁰. 在 nHz 频率下产生引力辐射的主要物理过程仍然不确定。脉冲星定时阵列观测目前无法²¹将双黑洞天体物理前景²²与宇宙学背景区分开来，因为，例如，在一个弱相互作用的暗区中，温度约为 1-100 MeV 的一阶相变^{8,9 ,10,11}。^{这封信探讨了结合宇宙微波背景23,24}、大爆炸核合成^25,26或天体测量^27,28观测的任意组合的超低频引力波谱的综合界限在多大程度上有助于打破这种退化。