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Abstract

The origin of the binary black hole mergers observed by LIGO-Virgo-KAGRA (LVK) remains intriguing. We consider a scenario that they are from mergers of primordial black holes (PBHs) within the density spikes around supermassive black holes (SMBHs) at the center of galaxies. The number of mergers between PBHs driven by gravitational wave (GW) emission in the spikes can be comparable to those within the whole dark matter halo. Meanwhile, the GW-driven mergers between PBHs and host SMBHs produce extreme mass ratio inspirals (EMRIs), which is the dominant merging channel compared to those driven by two-body relaxation. A correlation between the merger rates of EMRIs and PBH binaries can constrain PBH abundance. For PBHs of 30 M⊙ making up the whole dark matter spikes, we predict that LISA may detect ∼ 10^4 of these EMRIs with signal-to-noise ratio of 5 within a 4-year observation run. Uncertainties come from the PBH dark matter spike mass fraction relative to the host central SMBHs, which is the parameter space region LISA can constrain.