  Primary graviton spectra, produced via stimulated emission from an initial
Bose-Einstein distribution, are enhanced for typical scales larger than the
redshifted thermal wavelength. A mixed state of phonons induces a secondary
graviton spectrum which is hereunder computed in terms of three parameters
(i.e. the number of phonon species, the tensor-to-scalar ratio and the thermal
wavelengths of the mixture). The primary and secondary graviton spectra are
shown to be sensitive, respectively, to the first-order and second-order
correlation properties of the initial quantum mixture so that the semiclassical
theory is argued to be generally inadequate in this context. For particular
values of the parameters the secondary contribution may turn out to be
comparable with the primary spectrum over large-scales.
