Secondary graviton spectra, second-order correlations and Bose-Einstein enhancement

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.