  There are no reasons 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 are quintessential inflationary
models 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 studied the case of quintessential gravitons. The
minimum achievable sensitivity to $h^2_{0} \Omega_{GW}$ of different pairs of
detectors is computed, and compared with the theoretical expectations.

General Relativity and Quantum Cosmology;Astrophysics;High Energy Physics - Phenomenology