The stochastic gravitational wave background from primordial gravitational atoms

We propose a scenario of primordial gravitational atoms (PGAs), which may exist in the current and past universe due to spinning primordial black holes (PBHs) and very light bosonic fields. In a monochromatic mass scenario with a sizable dimensionless spin, which may arise in a short matter dominated (MD) era, we analyze the resulting stochastic gravitational wave background (SGWB) signal. Its spectrum is approximately characterized by a rising ∝ f3 followed by a falling ∝ f-1 where f is the frequency. Then, we investigate the constraints and prospects of such an SGWB, and find that PGAs with a core mass MBH ∼ 𝒪(10) M⊙ and a cloud of light scalar with mass μ ∼ 𝒪 (10-13) eV could yield constraints even stronger than those from bare PBHs. Future detectors such as LISA, Taiji and TianQin are able to explore PGAs over a narrow and elongated strap in the (μ,MBH) plane, spanning over 10 orders of magnitude for the maximum spin, 10-8M⊙ ≲ MBH ≲ 104M⊙, 10-16 eV ≲ μ ≲ 10-3 eV. If the PGA is dressed with a vector cloud, the SGWB signal has a much better opportunity to be probed.