Thermal history of the plasma and high-frequency gravitons

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 is 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.