Stochastic backgrounds of relic gravitons, T$\Lambda$CDM paradigm and the stiff ages

Absent any indirect tests on the thermal history of the Universe prior to the formation of light nuclear elements, it is legitimate to investigate situations where, before nucleosyntheis, the sound speed of the plasma was larger than $c/\sqrt{3}$, at most equalling the speed of light $c$. In this plausible extension of the current cosmological paradigm, hereby dubbed Tensor-$\Lambda$CDM (i.e. T$\Lambda$CDM) scenario, high-frequency gravitons are copiously produced. Without conflicting with the bounds on the tensor to scalar ratio stemming from the combined analysis of the three standard cosmological data sets (i.e. cosmic microwave background anisotropies, large-scale structure and supenovae), the spectral energy density of the relic gravitons in the T$\Lambda$CDM scenario can be potentially observable by wide-band interferometers (in their advanced version) operating in a frequency window which ranges between few Hz and few kHz.