A Non-Holomorphic Modular $A_4$ Framework for Resonant Leptogenesis with Gravitational Wave Signatures

Abstract

We study a type-I seesaw framework based on non-holomorphic $A_4$ modular symmetry, where polyharmonic Maa\ss\ forms construct the Yukawa couplings and right-handed neutrino (RHN) Majorana mass matrix. The use of non-holomorphic modular forms yields highly constrained neutral lepton mass matrices with a more restrictive lepton-sector structure and naturally generates a quasi-degenerate RHN mass spectrum, enabling resonant leptogenesis at an intermediate scale with RHN masses of $\mathcal{O}(10^3)$ TeV without requiring an ad hoc mass degeneracy. We further extend the model by introducing a complex scalar field $(\Phi)$ charged under $\mathbb{Z}_3$ symmetry. The spontaneous breaking of the discrete symmetry after the phase transition associated with $\Phi$ leads to domain-wall (DW) formation. A radiatively induced bias term associated with the RHN sector triggers DW annihilation, resolving the cosmological DW problem, and producing a stochastic gravitational wave (GW) signal that indirectly probes the RHN mass scale. The accompanying first-order phase transition produces a second GW peak, yielding a characteristic double-peaked spectrum with frequencies separated by several orders of magnitude and potentially observable by complementary future GW detectors.