Majoron Phenomenology in a Radiative Inverse Seesaw Embedded in an Extended Inert Doublet Model

We study the phenomenology of the Majoron in a radiative inverse seesaw framework embedded in an extended inert doublet model. In this setup, the lepton-number-violating parameter [Formula: see text] is generated at the two-loop level, leading to naturally suppressed Majoron couplings to light neutrinos. We derive the Majoron interaction matrix in the neutrino mass basis and compute decay widths for processes such as [Formula: see text], [Formula: see text], and [Formula: see text]. We find that the couplings involving light neutrinos are highly suppressed, rendering their invisible decays negligible.For heavy neutral fermions, Majoron-induced decays are controlled by [Formula: see text] and are typically subdominant compared to gauge-mediated channels. For representative values with sizable light–heavy mixing, heavy neutrinos decay promptly, while in regions with suppressed mixing the Majoron channels can become relatively important, leading to reduced visible branching ratios, enhanced missing-energy signatures, and potentially long-lived particles. Finally, we show that the Majoron never thermalizes in the early Universe, so that its contribution to the radiation energy density is negligible, ensuring consistency with BBN and CMB bounds on [Formula: see text].