Next-generation tests of fundamental physics and cosmology using large scale structure require measurements over large volumes of the Universe, including high redshifts inaccessible to present-day surveys. Line intensity mapping, an emerging technique that detects the integrated emission of atomic and molecular lines without resolving sources, can efficiently map cosmic structure over a wide range of redshifts. Observations at millimeter wavelengths detect far-IR emission lines such as CO/[CII], and take advantage of observational and analysis techniques developed by CMB experiments. These measurements can provide constraints with unprecedented precision on the physics of inflation, neutrino masses, light relativistic species, dark energy and modified gravity, and dark matter, among many other science goals. In this white paper we forecast the sensitivity requirements for future ground-based mm-wave intensity mapping experiments to enable transformational cosmological constraints. We outline a staged experimental program to steadily improve sensitivity, and describe the necessary investments in developing detector technology and analysis techniques.