  Possible deviations from a radiation-dominated evolution, occurring prior the
synthesis of light nuclei, impacted on the spectral energy density of
high-frequency gravitons. For a systematic scrutiny of this situation, the
$\Lambda$CDM paradigm must be complemented by (at least two) physical
parameters describing, respectively, a threshold frequency and a slope. The
supplementary frequency scale sets the lower border of a high-frequency domain
where the spectral energy grows with a slope which depends, predominantly, upon
the total sound speed of the plasma right after inflation. While the infra-red
region of the graviton energy spectrum is nearly scale-invariant, the expected
signals for typical frequencies larger than 0.01 nHz are hereby analyzed in a
model-independent framework by requiring that the total sound speed of the
post-inflationary plasma be smaller than the speed of light. Current (e.g.
low-frequency) upper limits on the tensor power spectra (determined from the
combined analysis of the three large-scale data sets) are shown to be
compatible with a detectable signal in the frequency range of wide-band
interferometers. In the present context, the scrutiny of the early evolution of
the sound speed of the plasma can then be mapped onto a reliable strategy of
parameter extraction including not only the well established cosmological
observables but also the forthcoming data from wide band interferometers.
