Axion-like particle (ALP) portal freeze-in dark matter confronting ALP search experiments

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.