The Standard Model (SM) is inadequate to explain the origin of tiny neutrino masses, the dark matter (DM) relic abundance and also the baryon asymmetry of the Universe. In this work to address all the three puzzles, we extend the SM by a local U$(1)_{rm B-L}$ gauge symmetry, three right-handed (RH) neutrinos for the cancellation of gauge anomalies and two complex scalars having nonzero U$(1)_{rm B-L}$ charges. All the newly added particles become massive after the breaking of U$(1)_{rm B-L}$ symmetry by the vacuum expectation value (VEV) of one of the scalar fields $phi_H$. The other scalar field $phi_{DM}$, which does not have any VEV, becomes automatically stable and can be a viable DM candidate. Neutrino masses are generated using Type-I seesaw mechanism while the required lepton asymmetry to reproduce the observed baryon asymmetry, can be attained from the CP violating out of equilibrium decays of RH neutrinos in TeV scale. More importantly within this framework, we have studied in detail the production of DM via freeze-in mechanism considering all possible annihilation and decay processes. Finally, we find a situation when DM is dominantly produced from the annihilation of RH neutrinos, which are at the same time also responsible for neutrino mass generation and leptogenesis.
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