  If the refractive index of the tensor modes increases during a conventional
inflationary stage of expansion the relic graviton spectrum is tilted towards
high frequencies. Two apparently diverse parametrizations of this effect are
shown to be related by a rescaling of the four-dimensional metric through a
conformal factor that involves the refractive index itself. Non-monotonic
spectra with a maximum in the MHz region correspond to a limited variation of
the refractive index terminating well before the end of inflation. After
exploring a general approach encompassing the ones proposed so far, we estimate
the required sensitivity for the direct detection of the predicted
gravitational radiation and demonstrate that the allowed regions of the
parameter space are within reach for some of the planned detectors operating
either in the audio band (like Ligo/Virgo and Kagra) or in the mHz band (like
Lisa, Bbo and Decigo).
