The Role of Radio Observations in Studies of Infrared-Bright Galaxies: Prospects for a next-generation Very Large Array

The bulk of the present-day stellar mass was formed in galaxies when the universe was less than half its current age (i.e., $1 \lesssim z \lesssim 3$). While this likely marks one of the most critical time periods for galaxy evolution, we currently do not have a clear picture on the radial extent and distribution of cold molecular gas and associated star formation within the disks of galaxies during this epoch. Such observations are essential to properly estimate the efficiency at which such galaxies convert their gas into stars, as well as to account for the various energetic processes that govern this efficiency. Long-wavelength (i.e., far-infrared--to--radio) observations are critical to penetrate the high-levels of extinction associated with dusty, infrared-bright galaxies that are driving the stellar mass assembly at such epochs. In this article we discuss how the next-generation Very Large Array will take a transformative step in our understanding of galaxy formation and evolution by delivering the ability to simultaneously study the relative distributions molecular gas and star formation on sub-kpc scales unbiased by dust for large populations of typical galaxies in the early universe detected by future far-infrared space missions.