Stimulated emission of relic gravitons and their super-Poissonian statistics

The degree of second-order coherence of the relic gravitons produced from the vacuum is super-Poissonian and larger than in the case of a chaotic source characterized by a Bose–Einstein distribution. If the initial state does not minimize the tensor Hamiltonian and has a dispersion smaller than its averaged multiplicity, the overall statistics is by definition sub-Poissonian. Depending on the nature of the sub-Poissonian initial state, the final degree of second-order coherence of the quanta produced by stimulated emission may diminish (possibly even below the characteristic value of a chaotic source) but it always remains larger than one (i.e. super-Poissonian). When the initial statistics is Poissonian (like in the case of a coherent state or for a mixed state weighted by a Poisson distribution) the degree of second-order coherence of the produced gravitons is still super-Poissonian. Even though the quantum origin of the relic gravitons inside the Hubble radius can be effectively disambiguated by looking at the corresponding Hanbury Brown–Twiss correlations, the final distributions caused by different initial states maintain their super-Poissonian character which cannot be altered.