Flat spectra of cosmic gravitons in the nHz and audio bands

The spectra of the relic gravitons are customarily normalized in the low-frequency domain where the signal of the concordance paradigm is expected to peak and this is why their contribution to the temperature and polarization anisotropies of the microwave background is only described by the tensor to scalar ratio. If the consistency relations are broken, the same strategy is accomplished by introducing the tensor spectral index as a further independent parameter. When the dominant component of the spectral energy density is distributed for frequencies much larger than the aHz, the logic behind this conventional approach is much less compelling. The improved bounds in the audio band and the current data from the pulsar timing arrays in the nHz region motivate a new strategy for the absolute normalization of the cosmic background of relic gravitons. After introducing a general four-dimensional action for the analysis of the relic gravitons the new approach is illustrated in the case of conventional and unconventional inflationary models.