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 ∼ 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.kAlexander D. Dolgov:

In this work, we present the first experimental upper limits on the presence of stochastic ultrahigh-frequency gravitational waves. We exclude gravitational waves in the frequency bands from (2.7−14)×10 14 Hz and (5−12)×10 18 Hz down to a characteristic amplitude of h min c ≈ 6×10 −26 and h min c ≈ 5 × 10 −28 at 95% confidence level, respectively. To obtain these results, we used data from existing facilities that have been constructed and operated with the aim of detecting WISPs (Weakly Interacting Slim Particles), pointing out that these facilities are also sensitive to gravitational waves by graviton to photon conversion in the presence of a magnetic field. The principle applies to all experiments of this kind, with prospects of constraining (or detecting), for example, gravitational waves from light primordial black hole evaporation in the early universe.

Conversion of gravitational waves into electromagnetic radiation is discussed. The probability of transformations of gravitons into photons in presence of cosmological background magnetic field is calculated at the recombination epoch and during subsequent cosmological stages. The produced electromagnetic radiation is concentrated in the X-ray part of the spectrum. It is shown that if the early Universe was dominated by primordial black holes (PBHs) prior to Big Bang Nucleosynthesis (BBN), the relic gravitons emitted by PBHs would transform to an almost isotropic background of electromagnetic radiation due to conversion of gravitons into photons in cosmological magnetic fields. Such extragalactic radiation could be noticeable or even dominant component of Cosmic X-ray Background.