Relic gravitons and high-frequency detectors

Cosmic gravitons are expected in the MHz-GHz regions that are currently unreachable by the operating wide-band interferometers and where various classes of electromechanical detectors have been proposed through the years. The minimal chirp amplitude detectable by these instruments is often set on the basis of the sensitivities reachable by the detectors currently operating in the audio band. By combining the observations of the pulsar timing arrays, the limits from wide-band detectors and the other phenomenological bounds we show that this requirement is far too generous and even misleading since the actual detection of relic gravitons well above the kHz would demand chirp and spectral amplitudes that are ten or even fifteen orders of magnitude smaller than the ones currently achievable in the audio band, for the same classes of stochastic sources. We then examine more closely the potential high-frequency signals and show that the sensitivity in the chirp and spectral amplitudes must be even smaller than the ones suggested by the direct and indirect constraints on the cosmic gravitons. We finally analyze the high-frequency detectors in the framework of Hanbury-Brown Twiss interferometry and argue that they are actually more essential than the ones operating in the audio band (i.e. between few Hz and few kHz) if we want to investigate the quantumness of the relic gravitons and their associated second-order correlation effects. We suggest, in particular, how the statistical properties of thermal and non-thermal gravitons can be distinguished by studying the corresponding second-order interference effects.