Induced gravitational waves probing primordial black hole dark matter with the memory burden effect
Kazunori Kohri, Takahiro Terada, Tsutomu T. Yanagida
Abstract
Quantum evaporation of a black hole is conventionally studied semiclassically by assuming self-similarity of the black hole throughout the evaporation process. However, its validity was recently questioned, and the lifetime of a black hole is conjectured to be much extended by the memory burden effect. It gives rise to the possibility that the primordial black holes (PBHs) lighter than ${10}^{10}$ grams are the dark matter in the Universe. To probe such PBH dark matter, we study gravitational waves (GWs) induced by primordial curvature perturbations that produced the PBHs. We find ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{GW}}({f}_{\mathrm{peak}}){h}^{2}=7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ with the peak frequency ${f}_{\mathrm{peak}}=1\ifmmode\times\else\texttimes\fi{}{10}^{3}({M}_{\mathrm{PBH}}/({10}^{10}\text{ }\text{ }\mathrm{g}){)}^{\ensuremath{-}1/2}\text{ }\text{ }\mathrm{Hz}$, and the induced GWs associated with the PBH dark matter whose initial mass is greater than about ${10}^{7}$ grams can be tested by future observations such as Cosmic Explorer. Furthermore, the scenario can be in principle confirmed by detecting another GW signal from the mergers of PBHs, which leads to high-frequency GWs with ${f}_{\mathrm{peak}}=2\ifmmode\times\else\texttimes\fi{}{10}^{27}({M}_{\mathrm{PBH},\mathrm{ini}}/({10}^{10}\text{ }\text{ }\mathrm{g}){)}^{\ensuremath{-}1}\text{ }\text{ }\mathrm{Hz}$. On the other hand, the induced GW signals stronger than expected would contradict the dark matter abundance and exclude the memory burden effect.