Cosmology with the SPHEREX All-Sky Spectral Survey

SPHEREx (Spectro-Photometer for the History of the Universe, Epoch of Reionization, and Ices Explorer) ( http://spherex.caltech.edu ) is a proposed all-sky spectroscopic survey satellite designed to address all three science goals in NASA's Astrophysics Division: probe the origin and destiny of our Universe; explore whether planets around other stars could harbor life; and explore the origin and evolution of galaxies. SPHEREx will scan a series of Linear Variable Filters systematically across the entire sky. The SPHEREx data set will contain R=40 spectra fir 0.75$<\lambda<$4.1$\mu$m and R=150 spectra for 4.1$<\lambda<$4.8$\mu$m for every 6.2 arc second pixel over the entire-sky. In this paper, we detail the extra-galactic and cosmological studies SPHEREx will enable and present detailed systematic effect evaluations. We also outline the Ice and Galaxy Evolution Investigations.