Impact of high-scale Seesaw and Leptogenesis on inflationary tensor perturbations as detectable gravitational waves

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.