The refractive index of the relic gravitons and the nHz band
  If the refractive index of the relic gravitons increases during a
conventional stage of inflationary evolution the spectral energy density is
blue at intermediate frequencies above the fHz and then flattens out after a
knee that is typically smaller than the mHz. We investigate here the conditions
leading to a sufficiently large spectral energy density in the nHz range where
some peculiar signatures observed with the pulsar timing arrays have been
recently attributed to cosmic gravitons. If these potential evidences are
combined with the most recent bounds provided by wide-band interferometers in
the audio range (i.e. between few Hz and the kHz) the allowed regions of the
parameter space are compatible with both determinations and also with all the
other constraints associated with the background of relic gravitons produced
during inflation. The present analysis suggests that the pulsar timing arrays
are sensitive to the evolution of the refractive index during the early stages
of the inflationary evolution. This physical interpretation of the preliminary
empirical evidence is distinguishable from other perspectives since the
high-frequency normalization, the blue spectral index and the tensor to scalar
ratio cannot be independently assigned but are all related to the frequency of
the knee that is ultimately determined by the competition between the rate of
evolution of the refractive index and the slow-roll corrections.
