Ultra-high frequency spikes of relic gravitons

The maximal frequency domain of the cosmic gravitons falls in the THz region where, without conflicting with the existing phenomenological bounds, only few particles with opposite (comoving) three-momenta are produced. As a consequence, the spectral energy density of the produced species peaks in the THz range, with features that depend upon the post-inflationary expansion rate. Although any reliable scrutiny of the ultra-high frequency spikes should include all the sources of late-time suppression at lower and intermediate frequencies, some relevant properties of the averaged multiplicities and of the spectral energy density can be derived within a reduced set of approximations that may become invalid as the frequency decreases well below the Hz. The accuracy of these concurrent approaches is assessed from the properties of the transition matrix that relates the late-time spectra to the values of the mode functions during an inflationary stage. In the obtained framework the bounds on the post-inflationary expansion rate are swiftly deduced and compare quite well with the ones including a more faithful numerical treatment. It also follows that the timeline of the post-inflationary expansion rate might be observationally accessible, in the years to come, provided the electromechanical detectors (like microwave cavities or waveguides) operating between the MHz and the THz shall eventually reach sensitivities in the chirp amplitudes which are (at least) twelve orders of magnitude smaller than the ones experimentally attainable in the audio band (i.e. between few Hz and the kHz).