  The dynamical evolution of the refractive index of the tensor modes of the
geometry produces a specific class of power spectra characterized by a blue
(i.e. slightly increasing) slope which is directly determined by the
competition of the slow-roll parameter and of the rate of variation of the
refractive index. Throughout the conventional stages of the inflationary and
post-inflationary evolution, the microwave background anisotropies
measurements, the pulsar timing limits and the big-bang nucleosythesis
constraints set stringent bounds on the refractive index and on its rate of
variation. Within the physically allowed region of the parameter space the
cosmic background of relic gravitons leads to a potentially large signal for
the ground based detectors (in their advanced version) and for the proposed
space-borne interferometers. Conversely, the lack of direct detection of the
signal will set a qualitatively new bound on the dynamical variation of the
refractive index.
