  The relic density of Dark Matter (DM) in the freeze-in scenario is highly
dependent on the evolution history of the universe and changes significantly in
a non-standard (NS) cosmological framework prior to Big Bang Nucleosynthesis
(BBN). In this scenario, an additional species dominates the energy budget of
the universe at early times (before BBN), resulting in a larger cosmological
expansion rate at a given temperature compared to the standard
radiation-dominated (RD) universe. To investigate the production of DM in the
freeze-in scenario, we consider both standard RD and NS cosmological picture
before BBN and perform a comparative analysis. We extend the Standard Model
(SM) particle content with a SM singlet DM particle $\chi $ and an axion-like
particle (ALP) $a$. The interactions between ALP, SM particles, and DM are
generated by higher dimensional effective operators. This setup allows the
production of DM $\chi$ from SM bath through the mediation of ALP, via
ALP-portal processes. These interactions involve non-renormalizable operators,
leading to ultraviolet (UV) freeze-in, which depends on the reheating
temperature ($T_{RH}$) of the early universe. In the NS cosmological scenario,
the faster expansion rate suppresses the DM production processes, allowing for
enhanced effective couplings between the visible and dark sectors to satisfy
the observed DM abundance compared to RD scenario. This improved coupling
increases the detection prospects for freeze-in DM via the ALP-portal, which is
otherwise challenging to detect in RD universe due to small couplings involved.
Using an effective field theory set-up, we show that various ALP searches such
as in FASER, DUNE, and SHiP, etc. will be able to probe significant parameter
space depending on the different model parameters.
