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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 a SGWB, and find that PGAs with a core mass M ₁₇ O (10) ~M_ and a cloud of light scalar with mass 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 (, M ₁₇) plane, spanning over 10 orders of magnitude for the maximum spin, 10^-8~M_ M ₁₇ 10⁴~M_, 10^-16~ eV 10^-3~ eV. If the PGA is dressed with a vector cloud, the SGWB signal has a much better opportunity to be probed.
Kang et al. (Thu,) studied this question.