  We show that the maximal frequency of cosmic gravitons must not exceed the
THz domain. From a classical viewpoint, both in conventional inflationary
scenarios and in bouncing models the largest frequency of the spectrum
overshoots the MHz band even if its specific signature is model dependent.
According to a quantum mechanical perspective the maximal frequency is instead
associated with the range of energies where a single pair of gravitons with
opposite (comoving) three-momenta is produced. The upper limit on the largest
frequency determines the minimal chirp amplitude [typically ${\mathcal
O}(10^{-32})$] required for a direct detection of a cosmic signal in the THz
band. Below this limiting frequency the minimal chirp amplitude can be enhanced
so that the optimal range ultimately depends on the physical properties of the
diffuse backgrounds. In case a hypothetical instrument (at present just a
figment of a hopeful imagination) would reach chirp amplitudes down to
${\mathcal O}(10^{-30})$ in the MHz or GHz bands, the Bose-Einstein
correlations could be used to probe the properties of cosmic gravitons and
their super-Poissonian statistics.
