Induced gravitational waves from the cosmic coincidence

The induced gravitational wave (GW) background from enhanced primordial scalar perturbations is one of the most promising observational consequences of primordial black hole (PBH) formation from inflation. We investigate the induced GW spectrum $\Omega_{\textrm{IGW}}$ from single-field inflation in the general ultra-slow-roll (USR) framework, restricting the peak frequency band to be inside $10^{-3}$-$1$ Hz and saturating PBH abundance to comprise all dark matter (DM) in the ultralight asteroid-mass window. By invoking successful baryogenesis driven by USR inflation, we verify the viable parameter space for the specific density ratio between baryons and PBH DM observed today, the so-called "cosmic coincidence." We show that the cosmic coincidence requirement bounds the spectral index $n_{\rm UV}$ in the high frequency limit, $\Omega_{\textrm{IGW}}(f\gg 1)\propto f^{-2n_{\rm UV}}$, into $0 < n_{\rm UV} < 1$, which implies that baryogenesis triggered by USR inflation for PBHs in the mass range of $10^{-16}$-$10^{-12} M_\odot$ can be tested by upcoming Advanced LIGO and Virgo data and next generation experiments such as LISA, Einstein Telescope, TianQin and DECIGO.