  The low-frequency gravitons correspond to typical wavelengths that left the
Hubble radius during the early inflationary stages of expansion and reentered
after matter radiation equality. Consequently the temperature and the
polarization anisotropies of the cosmic microwave background constrain the
tensor-to-scalar-ratio in the aHz region but since the audio band and the MHz
domain are sensitive to the post-inflationary expansion rate, the low-frequency
determinations of the tensor-to-scalar-ratio can be combined with the
high-frequency constraints. In this framework we examine the possibility that
the low-frequency gravitons remain invisible in the aHz region but are still
potentially detectable at much higher frequencies. Because the number of
$e$-folds associated with the exit of the cosmic microwave background
wavelengths depends both on the slow-roll parameters and on the total expansion
rate after inflation, this approach leads to a set of lower bounds on the
tensor-to-scalar-ratio.
