Induced gravitational wave background and primordial black holes

We calculate the frequency dependence of gravitational wave background arising at second order of cosmological perturbation theory due to mixing of tensor and scalar modes. The calculation of the induced gravitational background is performed for two special cases: for the power spectrum of scalar perturbations which has a peak at some scale and for the scalar spectrum predicted by the inflationary model with the running mass potential. We show that the amplitudes of the induced gravitational background, in the frequency region $\sim 10^{-3} - 10^3 $Hz, are effectively constrained by results of studies of primordial black hole production in early universe. We argue that though today's LIGO bound on ${\cal P}_{\cal R}(k)$ is weaker than the PBH one, Advanced LIGO will be able to set a stronger bound, and in future the ground-based interferometers of LIGO type will be suitable for obtaining constraints on PBH number density in the mass range $\sim 10^{11} - 10^{15}$ g.