  We explore the dark matter freeze-in mechanism within the gauge mediation
framework, which involves a hidden Feebly Interacting Massive Particle (FIMP)
coupling feebly with the messenger fields while the messengers are still in the
thermal bath. The FIMP is the fermionic component of the pseudo-moduli in a
generic metastable supersymmetry (SUSY) breaking model and resides in the
hidden sector. The relic abundance and the mass of the FIMP are determined by
the SUSY breaking scale and the feeble coupling. The gravitino, which is the
canonical dark matter candidate in the gauge mediation framework, contributes
to the dark matter relic abundance along with the freeze-in of the FIMP. The
hidden sector thus becomes two- component with both the FIMP and gravitino
lodging in the SUSY breaking hidden sector. We point out that the ratio between
the FIMP and the gravitino is determined by how SUSY breaking is communicated
to the messengers. In particular when the FIMP dominates the hidden sector, the
gravitino becomes the minor contributor in the hidden sector. Meanwhile, the
neutralino is assumed to be both the Weakly Interacting Massive Particle (WIMP)
dark matter candidate in the freeze-out mechanism and the Lightest Observable
SUSY Particle (LOSP). We further find out the neutralino has the sub-leading
contribution to the current dark matter relic density in the parameter space of
our freeze-in gauge mediation (FIGM) model. Our result links the SUSY breaking
scale in the gauge mediation framework with the FIMP freeze-in production rate
leading to a natural and predicting scenario for the studies of the dark matter
in the hidden sector.
