  We investigate the impact of the post-inflationary thermal histories on the
cosmic graviton spectrum caused by the inflationary variation of their
refractive index. Depending on the frequency band, the spectral energy
distribution can be mildly red, blue or even violet. Wide portions of the
parameter space lead to potentially relevant signals both in the audio range
(probed by the advanced generation of terrestrial interferometers) and in the
mHz band (where space-borne detectors could be operational within the incoming
score year). The description of the refractive index in conformally related
frames is clarified.
