Cosmological Consequences of a Highly Decoupled Right-handed Neutrino

In the minimal type-I seesaw, one right-handed neutrino (RHN) can decouple from neutrino mass generation. Such a state is usually neglected, yet its feeble couplings make it long-lived, and it can dominate the energy density of the Universe before decaying. We study this in a minimal $U(1{)}_{B-L}$ model, where the RHNs are produced through $B-L$ gauge interactions, for the cases of a decoupled lightest RHN $N_1$ and a decoupled heaviest RHN $N_3$. The resulting early matter-dominated era dilutes the baryon asymmetry, and for decoupled $N_3$ it also delays the equilibration of the charged-lepton Yukawa interactions, allowing a lighter $N_1$ to generate the asymmetry in the unflavoured regime. Breaking $U(1{)}_{B-L}$ forms cosmic strings whose gravitational-wave background acquires a spectral break from the early matter-dominated era, with a frequency set by the decoupled RHN mass and the lightest neutrino mass, within reach of future detectors such as SKA, THEIA, LISA, $\mu$ARES, DECIGO and ET.