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If the refractive index of the relic gravitons increases during aconventional stage of inflationary evolution the spectral energy density isblue at intermediate frequencies above the fHz and then flattens out after aknee that is typically smaller than the mHz. We investigate here the conditionsleading to a sufficiently large spectral energy density in the nHz range wheresome peculiar signatures observed with the pulsar timing arrays have beenrecently attributed to cosmic gravitons. If these potential evidences arecombined with the most recent bounds provided by wide-band interferometers inthe audio range (i.e. between few Hz and the kHz) the allowed regions of theparameter space are compatible with both determinations and also with all theother constraints associated with the background of relic gravitons producedduring inflation. The present analysis suggests that the pulsar timing arraysare sensitive to the evolution of the refractive index during the early stagesof the inflationary evolution. This physical interpretation of the preliminaryempirical evidence is distinguishable from other perspectives since thehigh-frequency normalization, the blue spectral index and the tensor to scalarratio cannot be independently assigned but are all related to the frequency ofthe knee that is ultimately determined by the competition between the rate ofevolution of the refractive index and the slow-roll corrections.

The refractive index of the relic gravitons and the nHz band