  Gas density is widely believed to play a governing role in star formation.
However, the exact role of density in setting the star formation rate remains
debated. We also lack a general theory that explains how the gas density
distribution in galaxies is set. The primary factor preventing the resolution
of these issues is the limited number of observations of the gas density
distribution across diverse environments. Centimeter- and millimeter-wave
spectroscopy offer the most promising way forward in this field, but the key
density-sensitive transitions are faint compared to the capabilities of current
telescopes. In this chapter, we describe how a next-generation Very Large Array
(ngVLA) represents the natural next step forward in this sensitivity-limited
field. Such a facility would provide a crucial link between the `Milky Way' and
`Extragalactic' views of star formation and dramatically advance our
understanding of the drive and role of gas density in galaxies, building on
current results from ALMA, NOEMA, the Green Bank Telescope, and other current
facilities working in this area.
