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Relic gravitational waves from light primordial black holes

The energy density of relic gravitational waves (GWs) emitted by primordial black holes (PBHs) is calculated. We estimate the intensity of GWs produced at quantum and classical scattering of PBHs, the classical graviton emission from the PBH binaries in the early Universe, and the graviton emission due to PBH evaporation. If nonrelativistic PBHs dominated the cosmological energy density prior to their evaporation, the probability of formation of dense clusters of PBHs and their binaries in such clusters would be significant and the energy density of the generated gravitational waves in the present day universe could exceed that produced by other known mechanisms. The intensity of these gravitational waves would be maximal in the GHz frequency band of the spectrum or higher and makes their observation very difficult by present detectors but also gives a rather good possibility to investigate it by present and future high frequency gravitational waves electromagnetic detectors. However, the low frequency part of the spectrum in the range $f\sim 0.1-10$ Hz may be detectable by the planned space interferometers DECIGO/BBO. For sufficiently long duration of the PBH matter dominated stage the cosmological energy fraction of GWs from inflation would be noticeably diluted.