A Spectroscopic Road Map for Cosmic Frontier: DESI, DESI-II, Stage-5

In this white paper, we present an experimental road map for spectroscopic experiments beyond DESI. DESI will be a transformative cosmological survey in the 2020s, mapping 40 million galaxies and quasars and capturing a significant fraction of the available linear modes up to z=1.2. DESI-II will pilot observations of galaxies both at much higher densities and extending to higher redshifts. A Stage-5 experiment would build out those high-density and high-redshift observations, mapping hundreds of millions of stars and galaxies in three dimensions, to address the problems of inflation, dark energy, light relativistic species, and dark matter. These spectroscopic data will also complement the next generation of weak lensing, line intensity mapping and CMB experiments and allow them to reach their full potential.