Inflationary Gravitational Wave Spectral Shapes as test for Low-Scale Leptogenesis

We study thermal and non-thermal resonant leptogenesis in a general setting where a heavy scalar φ decays to right-handed neutrinos (RHNs) whose further out-of-equilibrium decay generates the required lepton asymmetry. Domination of the energy budget of the Universe by the φ or the RHNs alters the evolution history of the primordial gravitational waves (PGW), of inflationary origin, which re-enter the horizon after inflation, modifying the spectral shape. The decays of φ and RHNs release entropy into the early Universe while nearly degenerate RHNs facilitate low and intermediate scale leptogenesis. We show that depending on the coupling yR of φ to radiation species, RHNs can achieve thermal abundance before decaying, which gives rise to thermal leptogenesis. A characteristic damping of the GW spectrum resulting in two knee-like features or one knee-like feature would provide evidence for low-scale thermal and non-thermal leptogenesis respectively. We explore the parameter space for the lightest right-handed neutrino mass M₁∈[10²,10¹⁴] GeV and washout parameter K that depends on the light-heavy neutrino Yukawa couplings λ, in the weak ($K < 1$) and strong ($K > 1$) washout regimes. The resulting novel features compatible with observed baryon asymmetry are detectable by future experiments like LISA and ET. By estimating signal-to-noise ratio (SNR) for upcoming GW experiments, we investigate the effect of the scalar mass M_φ and reheating temperature T_φ, which depends on the φ-N Yukawa couplings yN.