CMB signature of non-thermal Dark Matter produced from self-interacting dark sector

The basic idea of this work is to achieve the observed relic density of a non-thermal dark matter(DM) and its connection with Cosmic Microwave Background (CMB) via additional relativistic degrees of freedom which are simultaneously generated during the period $T_{\rm BBN}~{\rm to}~T_{\rm CMB}$ from a long-lived dark sector particle. To realize this phenomena we minimally extend the type-I seesaw scenario with a Dirac fermion singlet($\chi$) and a complex scalar singlet ($\varphi$) which transform non-trivially under an unbroken symmetry $\mathcal{Z}_3$. $\chi$ being the lightest particle in the dark sector acts as a stable dark matter candidate while the next to lightest state $\varphi$ operates like a long lived dark scalar particle. The initial density of $\varphi$ can be thermally produced through either self-interacting number changing processes ($3 \varphi \to 2 \varphi$) within dark sector or the standard annihilation to SM particles ($2 \varphi \to 2~ {\rm SM}$). The late time (after neutrino decoupling) non-thermal decay of $\varphi$ can produce dark matter in association with active neutrinos. The presence of extra relativistic neutrino degrees of freedom at the time of CMB can have a significant impact on $\Delta \rm N_{eff}$. Thus the precise measurement of $\Delta \rm N_{ eff}$ by current PLANCK 2018 collaboration and future experiments like SPT-3G and CMB-S4 can indirectly probe this non-thermal dark matter scenario which is otherwise completely secluded due to its tiny coupling with the standard model.