Realization of self-interacting freeze-in dark matter

We explore the freeze-in production of dark matter in the singlet–doublet model where the dark matter is the lightest admixture of the neutral components of SU(2)_L vector doublet and singlet fermion. Here, the scalar sector is extended by a MeV scalar mediating the self-interaction of the fermion dark matter, which solves the small-scale anomaly of the Universe. The scalar particle is stable and contributes to the relic density of the dark matter. Self-interacting dark matter scenario demands large interaction between the dark particles, which makes this sector strongly coupled. In this case, thermal equilibrium occurs in the dark sector after the freeze-in, and the relic abundance of the fermion dark matter gets suppressed in the radiation-dominated early Universe. However, the non-standard cosmological evolution in the early Universe helped the fermion dark matter to achieve almost whole contribution towards the observed relic.