Sensitivity of wideband detectors to quintessential gravitons

Abstract

There is no reason why the energy spectra of the relic gravitons amplified by the pumping action of the background geometry should not increase at high frequencies. A typical example of this behavior is quintessential inflation where the slopes of the energy spectra can be either blue or mildly violet. In comparing the predictions of scenarios leading to blue and violet graviton spectra we face the problem of correctly deriving the sensitivities of the interferometric detectors. Indeed the expression of the signal-to-noise ratio not only depends upon the noise power spectra of the detectors but also upon the spectral form of the signal and, therefore, one can reasonably expect that models with different spectral behaviors will produce different signal-to-noise ratios. By assuming monotonic (blue) spectra of relic gravitons we will give general expressions for the signal-to-noise ratio in this class of models. As an example we study the case of quintessential gravitons. The minimum achievable sensitivity to ${h}_{0}^{2}{\ensuremath{\Omega}}_{\mathrm{GW}}$ of different pairs of detectors is computed, and compared with theoretical expectations.