Bound on induced gravitational wave background from primordial black holes

The today's energy density of the induced (second order) gravitational wave background in the frequency region $\sim\,10^{-3}$–$10^3$ Hz is constrained using the existing limits on primordial black hole production in the early Universe. It is shown, in particular, that at frequencies near $\sim\,40$ Hz (which is the region explored by LIGO detector), the value of the induced part of $\Omega_{GW}$ cannot exceed $(1$–$3)\cdot10^{-7}$. The spread of values of the bound is caused by the uncertainty in parameters of the gravitational collapse of black holes.