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

TL;DR

This paper investigates how initial quantum states and phonon mixtures influence secondary graviton spectra, revealing potential enhancements and the limitations of semiclassical theory in describing these phenomena.

Contribution

It computes the secondary graviton spectrum induced by phonon mixtures and analyzes its dependence on initial quantum correlations and parameters.

Findings

Secondary graviton spectra can be significantly enhanced for large scales.

The primary and secondary spectra are sensitive to different correlation properties.

Semiclassical theory may be inadequate for describing these quantum-induced effects.

Abstract

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.