Blue and violet graviton spectra from a dynamical refractive index
  We show that the spectral energy distribution of relic gravitons mildly
increases for frequencies smaller than the $\mu$Hz and then flattens out
whenever the refractive index of the tensor modes is dynamical during a
quasi-de Sitter stage of expansion. For a conventional thermal history the
high-frequency plateau ranges between the mHz and the audio band but it is
supplemented by a spike in the GHz region if a stiff post-inflationary phase
precedes the standard radiation-dominated epoch. Even though the slope is blue
at intermediate frequencies, it may become violet in the MHz window. For a
variety of post-inflationary histories, including the conventional one, a
dynamical index of refraction leads to a potentially detectable spectral energy
density in the kHz and in the mHz regions while all the relevant
phenomenological constraints are concurrently satisfied.
