ODIN: The LAE Ly{\alpha} Luminosity Function over Cosmic Time and Environmental Density

The ubiquity and relative ease of discovery make $2\lesssim z\lesssim 5$ Ly$\alpha$ emitting galaxies (LAEs) ideal tracers for cosmology. In addition, because Ly$\alpha$ is a resonance line, but frequently observed at large equivalent width, it is potentially a probe of galaxy evolution. The LAE Ly$\alpha$ luminosity function (LF) is an essential measurement for making progress on both of these aspects. Although several studies have computed the LAE LF, very few have delved into how the function varies with environment. The large area and depth of the One-hundred-deg$^2$ DECam Imaging in Narrowbands (ODIN) survey makes such measurements possible at the cosmic noon redshifts of z~2.4, ~3.1, and ~4.5. In this initial work, we present algorithms to rigorously compute the LAE LF and test our methods on the ~16,000 ODIN LAEs found in the extended COSMOS field. Using these limited samples, we find slight evidence that protocluster environments either suppress the numbers of very faint and very bright LAEs or enhance medium-bright LAEs in comparison to the field. We also find that the LF decreases in number density and evolves towards a steeper faint-end slope over cosmic time from z~4.5 to z~2.4.