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 $\propto f^3$ followed by a falling $\propto f^{-1}$ where $f$ is the frequency. Then, we investigate the constraints and prospects of such a SGWB, and find that PGAs with a core mass $M_{\rm BH}\sim {\cal O}(10)~M_{\odot}$ and a cloud of light scalar with mass $\mu \sim {\cal O} (10^{-13})$ 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 $(\mu,M_{\rm BH})$ plane, spanning over 10 orders of magnitude for the maximum spin, $10^{-8}~M_{\odot}\lesssim M_{\rm BH}\lesssim 10^4~M_{\odot}$, $10^{-16}~{\rm eV}\lesssim \mu\lesssim 10^{-3}~\rm eV$. If the PGA is dressed with a vector cloud, the SGWB signal has a much better opportunity to be probed.