Abstract
The coherence of the relic gravitons is investigated within a quantum mechanical perspective. After introducing the notion and the properties of the generalized Glauber correlators valid in the tensor case, the degrees of first- and second-order coherence are evaluated both inside and beyond the effective horizon. The inclusive approach (encompassing the polarizations of the gravitons) is contrasted with the exclusive approximation where the total intensity is calculated either from a single polarization or even from a single mode of the field. While the relic gravitons reentering the effective horizon after the end of a quasi-de Sitter stage of expansion are first-order coherent, the Hanbury Brown-Twiss correlations always exhibit a super-Poissonian statistics with different quantitative features that depend on the properties of their initial states and on the average over the tensor polarizations.
Highlights
As gravitational wave astronomy is opening a new observational window, the potential implications of the current developments for the stochastic backgrounds of relic gravitons are more accurately investigated
In a wide range of scenarios, the early evolution of the space-time curvature induces a stochastic background of primordial gravitational waves with a spectral energy density extending today from frequencies OðaHzÞ (i.e., 1 aHz 1⁄4 10−18 Hz) up to frequencies OðGHzÞ (i.e., 1 GHz 1⁄4 109 Hz)
With the goal of inspiring some of the future endeavors, it is interesting to analyze the degrees of quantum coherence of the relic gravitons in a systematic perspective similar to the one already attempted in the case of large-scale curvature inhomogeneities
Summary
As gravitational wave astronomy is opening a new observational window, the potential implications of the current developments for the stochastic backgrounds of relic gravitons are more accurately investigated. Even if a direct detection of relic gravitons is not behind the corner both for technical and conceptual reasons, the degree of quantum coherence of the large-scale correlations could be used to disambiguate their origin, at least in principle [7,18,19] In light of these ambitious targets, the present investigations are mandatory. The signal may sharply augment when the spectral energy density increases for frequencies larger than the mHz as it happens when the tensor modes of the geometry inherit a refractive index [24,25] or in the presence of stiff phases In these cases, it can happen that hc 1⁄4 Oð10−25Þ [24], while the chirp amplitude hc corresponding to the astronomical signals detected so far by the Ligo/Virgo Collaboration is Oð10−21Þ [20,21,22]. To make the analysis self-contained, the most relevant technical results have been relegated to Appendixes A and B
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