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 ${\mathrm{\Omega }}_{GW}$ cannot exceed $(1-3)\times {10}^{-7}$. The spread of values of the bound is caused by the uncertainty in parameters of the gravitational collapse of black holes.