Cosmic Strings Gravitational Wave Probe of Leptogenesis: Thermal, Non-thermal, Near-resonant and Flavourful

Breaking a global or local $U(1)_{\rm B-L}$ symmetry at high scales simultaneously generates Majorana masses for heavy right-handed neutrinos and produces a network of cosmic strings. The evolution and decay of these strings source a stochastic gravitational-wave background that may be probed by current and future gravitational-wave experiments, while the decays of the resulting massive right-handed neutrinos can generate the baryon asymmetry of the Universe via leptogenesis. We derive analytical bounds for successful leptogenesis with a global and a local $U(1)_{B-L}$ symmetry, separately finding an absolute lower bound on the lightest right-handed neutrino mass $M_1 > 1.74 \times 10^{8}\,\mathrm{GeV}$ for thermal initial conditions and $M_1 > \mathcal{O}(10^{6})\,\mathrm{GeV}$ for non-thermal initial conditions. Allowing for near-resonant leptogenesis relaxes these bounds to TeV scale in both cases making it a viable target at collider searches complementing the GW signals. Full flavour effects are included, and crucially, we determine the region where successful leptogenesis can be probed through gravitational-wave observations in upcoming experiments such as LISA and Einstein Telescope. Importantly, we find that flavour effects rescue regions of the parameter space that are ruled out due to current CMB or gravitational wave measurements.