  Light mediator to dark matter is favorable for several phenomena in
astro-particle physics such as core-cusp problem. Such a light mediator can be
decoupled from Standard Model in order not to threaten direct detection
constraint, which is generally realized by retard decay of mediator. Their
out-of-equilibrium decays can alter the conventional evolution of dark matter
via entropy dilution and BBN constraint. Dark Matter in this manner typically
requires precision calculation of freeze-out process considering different
temperatures evolution. If the mediator is light enough, dark matter bound
state can be formed by emitting a mediator radiatively as well as sommerfled
enhancement. The radiative bound state formation process is expected to affect
the dark matter annihilation cross section at percent level. We also put the
combination of large mass splitting between dark matter and mediator and retard
decay of mediator on the same theoretical footing, discuss the implication for
dark matter relic density in this hidden sector. We study this type of model
and illustrate its property by considering general next-to-minimal
supersymmetric standard model (NMSSM).
