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 proportional to f3 followed by a falling proportional to 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 M BH similar to O (10) M circle dot and a cloud of light scalar with mass mu similar to 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 (mu, MBH) plane, spanning over 10 orders of magnitude for the maximum spin, 10-8 M circle dot <= M BH <= 104 M circle dot, 10 - 16 eV <= mu <= 10-3 eV. If the PGA is dressed with a vector cloud, the SGWB signal has a much better opportunity to be probed.