Abstract
Owing to the analogy with the ordinary photons in the visible range of the electromagnetic spectrum, the Glauber theory is generalized to address the quantum coherence of the gauge field fluctuations parametrically amplified during an inflationary stage of expansion. The first and second degrees of quantum coherence of relic photons are then computed beyond the effective horizon defined by the evolution of the susceptibility. In the zero-delay limit the Hanbury Brown-Twiss correlations exhibit a super-Poissonian statistics which is however different from the conventional results of the single-mode approximation customarily employed, in quantum optics, to classify the coherence properties of visible light. While in the case of large-scale curvature perturbations the degrees of quantum coherence coincide with the naive expectation of the single-mode approximation, the net degree of second-order coherence computed for the relic photons diminishes thanks to the effect of the polarizations. We suggest that the Hanbury Brown-twiss correlations are probably the only tool to assess the quantum or classical origin of the large-scale magnetic fluctuations and of the corresponding curvature perturbations.
Highlights
The squeezed states of optical photons arise in a number of diverse physical situations all related to the quantum theory of the parametric amplification [1]
The applications of quantum optical techniques to the analysis of large-scale inhomogeneities has been firstly suggested by Grishchuk and collaborators in a class of problems involving the evolution of the tensor and scalar modes of the fourdimensional geometry [16,17,18]
The quantum theory of parametric amplification has been later applied to the case of relic photons [25] where the quantum optical analogy is even more compelling: in this case it is precisely the time variation of the susceptibility that plays the role of the laser pump often employed for the direct experimental preparation of the squeezed states in various classes of nonlinear materials
Summary
The squeezed states of optical photons arise in a number of diverse physical situations all related (directly or indirectly) to the quantum theory of the parametric amplification [1]. The quantum theory of parametric amplification has been later applied to the case of relic photons [25] where the quantum optical analogy is even more compelling: in this case it is precisely the time variation of the susceptibility that plays the role of the laser pump often employed for the direct experimental preparation of the squeezed states in various classes of nonlinear materials (see, e.g., [1,11,12] and [26]). The quantum theory of parametric amplification of the relic photons (and of the relic gravitons and relic phonons) is useful for treating the problem of initial data but it becomes essential for analyzing the higher-order correlations of the largescale fluctuations, as the quantum optical analogy clearly suggests. Various useful details have been relegated to the Appendix
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