  We discuss the damping of inflationary gravitational waves (GW) that re-enter
the horizon before or during an epoch, where the energy budget of the universe
is dominated by an unstable right handed neutrino (RHN), whose out of
equilibrium decay releases entropy. Starting from the minimal Standard Model
extension, motivated by the observed neutrino mass scale, with nothing more
than 3 RHN for the Seesaw mechanism, we discuss the conditions for high scale
leptogenesis assuming a thermal initial population of RHN. We further address
the associated production of potentially light non-thermal dark matter and a
potential component of dark radiation from the same RHN decay. One of our main
findings is that the frequency, above which the damping of the tensor modes is
potentially observable, is completely determined by successful leptogenesis and
a Davidson-Ibarra type bound to be at around $0.1\;\text{Hz}$. To quantify the
detection prospects of this GW background for various proposed interferometers
such as AEDGE, BBO, DECIGO, Einstein Telescope or LISA we compute the
signal-to-noise ratio (SNR). This allows us to investigate the viable parameter
space of our model, spanned by the mass of the decaying RHN $M_1 \gtrsim
2.4\times 10^8\;\text{GeV} \cdot \sqrt{2\times 10^{-7}\;\text{eV}/\tilde{m}_1}$
(for leptogenesis) and the effective neutrino mass parameterizing its decay
width $\tilde{m}_1< 2.9\times 10^{-7}\;\text{eV}$ (for RHN matter domination).
Thus gravitational wave astronomy is a novel way to probe both the Seesaw and
the leptogenesis scale, which are completely inaccessible to laboratory
experiments in high scale scenarios.
