The multiplicity distributions of the high frequency gravitons

Abstract

When the gravitons are created thanks to the variation of the space-time curvature the multiplicity distributions quantify the probability of producing a given number of species around the average occupation numbers of the underlying multiparticle states. The multiplicities of the relic gravitons are infinitely divisible and their analytical expressions encompass, in different regions of the physical parameters, the Poisson, Bose-Einstein, Gamma and Pascal probability distributions. Depending upon the post-inflationary timelines, the averaged multiplicities are controlled by the range of the comoving frequencies and they can be much larger in the GHz region than in the aHz domain where the temperature and polarization anisotropies of the microwave background set strict limits on the spectral energy density of the relic gravitons. Thanks to the absolute upper bound on the maximal frequency of the gravitons we can acknowledge that the averaged multiplicities are exponentially suppressed above the THz, where only few pairs of gravitons are independently created from the vacuum. The statistical properties of the produced particles can be finally interpreted in the light of the second-order interference effects and this perspective is quantitatively scrutinized by analyzing the associated quantum sensitivities. For putative instruments reaching spectral amplitudes $O\left({10}^{-35}\right)/\sqrt{\mathrm{Hz}}$ 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. Both from the theoretical and observational viewpoint it is unjustified to require the same sensitivities (e.g. $O\left({10}^{-21}\right)/\sqrt{\mathrm{Hz}}$) in the kHz and GHz domains.