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.
