Gravitational waves from primordial black hole isocurvature: the effect of non-Gaussianities

Ultra-light primordial black holes (PBHs) with masses $M_{\rm PBH}<5\times 10^8\mathrm{g}$ can dominate transiently the energy budget of the Universe and reheat the Universe through their evaporation taking place before Big Bang Nucleosynthesis. The isocurvature energy density fluctuations associated to the inhomogeneous distribution of a population of such PBHs can induce an abundant production of GWs due to second-order gravitational effects. In this work, we discuss the effect of primordial non-Gaussianity on the clustering properties of PBHs and study the effect of a clustered PBH population on the spectral shape of the aforementioned induced GW signal. In particular, focusing on local-type non-Gaussianity we find a double-peaked GW signal with the amplitude of the low-frequency peak being proportional to the square of the non-Gaussian parameter $\tau_\mathrm{NL}$. Remarkably, depending on the PBH mass $M_{\rm PBH}$ and the initial abundance of PBHs at formation time, i.e. $\Omega_\mathrm{PBH,f}$, this double-peaked GW signal can lie well within the frequency bands of forthcoming GW detectors, namely LISA, ET, SKA and BBO, hence rendering this signal falsifiable by GW experiments and promoting it as a novel portal probing the primordial non-Gaussianity.