Test the mergers of the primordial black holes by high frequency gravitational-wave detector

The black hole could have a primordial origin if its mass is less than $$1M_\odot $$. The mergers of these black hole binaries generate stochastic gravitational-wave background (SGWB). We investigate the SGWB in high frequency band $$10^{8}$$–$$10^{10}\,\mathrm {Hz}$$. It can be detected by high frequency gravitational-wave detector. Energy density spectrum and amplitude of the SGWB are derived. The upper limit of the energy density spectrum is around $$10^{-7}$$. Also, the upper limit of the amplitude ranges from $$10^{-31.5}$$ to $$10^{-29.5}$$. The fluctuation of spacetime origin from gravitational wave could give a fluctuation of the background electromagnetic field in a high frequency gravitational-wave detector. The signal photon flux generated by the SGWB in the high frequency band $$10^{8}$$–$$10^{10}\,\mathrm {Hz}$$ is derived, which ranges from 1 to $$10^2\,\mathrm {s^{-1}}$$. The comparison between the signal photon flux generated by relic gravitational waves (RGWs) and the SGWB is also discussed in this paper. It is shown that the signal photon flux generated by the RGW, which is predicted by the canonical single-field slow-roll inflation models, is sufficiently lower than the one generated by the SGWB in the high frequency band $$10^{8}$$–$$10^{10}\,\mathrm {Hz}$$. Our results indicate that the SGWB in the high frequency band $$10^{8}$$–$$10^{10}\,\mathrm {Hz}$$ is more likely to be detected by the high frequency gravitational-wave detector