Understanding the Evolution of Black Hole Accretion and Dust out to z=4 with a Deep Imaging Extragalactic Survey with PRIMA

The cosmic evolution of obscured star formation, dust properties and production mechanisms, and the prevalence of dust-obscured AGN out to high redshifts are currently some of the hot topics in astrophysics. While much progress has been made in the early days with Spitzer and Herschel, these facilities have not reached the necessary depths to observe the mid-IR light of high-redshift (z > 3) galaxies. Recently, the James Webb Space Telescope (JWST) has filled in the blue side of the rest-frame mid-IR. The Atacama Large (Sub)Millimeter Array (ALMA), on the other hand, provides excellent sensitivity in the far-IR regime, allowing the study of dust and gas properties at high redshifts. Filling the wavelength gap between JWST and ALMA is crucial to progress our understanding of early galaxy evolution - and this will be an important goal in the next decades. The Probe far-IR Mission for Astrophysics (PRIMA), with sensitive imaging and spectroscopic capabilities at 24-240$\mu$m and currently in Phase A study, will achieve this and provide insights into early galaxy evolution, Black Hole growth, and dust production mechanisms. Here we present PRIDES, a possible deep and wide-area survey over 1.6 square-degrees of the COSMOS field with PRIMA to study these science cases.