Gravitational Wave Production right after a Primordial Black Hole
  Evaporation
  We discuss the footprint of evaporation of primordial black holes (PBHs) on
stochastic gravitational waves (GWs) induced by scalar perturbations. We
consider the case where PBHs once dominated the Universe but eventually
evaporated before the big bang nucleosynthesis. The reheating through the PBH
evaporation could end with a sudden change in the equation of state of the
Universe compared to the conventional reheating caused by particle decay. We
show that this "sudden reheating" by the PBH evaporation enhances the induced
GWs, whose amount depends on the length of the PBH-dominated era and the width
of the PBH mass function. We explore the possibility to constrain the
primordial abundance of the evaporating PBHs by observing the induced GWs. We
find that the abundance parameter $\beta \gtrsim 10^{-5} \text{ - }10^{-8}$ for
$\mathcal{O}(10^3 \text{ - } 10^5) \, \text{g}$ PBHs can be constrained by
future GW observations if the width of the mass function is smaller than about
a hundredth of the mass.
