SPHEREx (Spectro-Photometer for the History of the Universe, Epoch of Reionization, and Ices Explorer) [Website] 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< λ <4.1µm and R=150 spectra for 4.1< λ <4.8µm for every 6.2 arcsecond 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. I. SPHEREX MISSION OVERVIEWSPHEREx (Spectro-Photometer for the History of the Universe, Epoch of Reionization, and Ices Explorer; PI: J. Bock) is a proposed all-sky 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. All of these exciting science themes are addressed by a single survey, with a single instrument, providing the first near-infrared spectroscopy of the complete sky. In this paper, we will focus on the cosmological science enabled by SPHEREx and outline the Galactic Ices and the Epoch of Reionization (EOR) scientific investigations.SPHEREx will probe the origin of the Universe by constraining the physics of inflation, the superluminal expansion of the Universe that took place some 10 −32 s after the Big Bang. SPHEREx will study its imprints in the threedimensional large-scale distribution of matter by measuring galaxy redshifts over a large cosmological volume at low redshifts, complementing high-redshift surveys optimized to constrain dark energy.SPHEREx will investigate the origin of water and biogenic molecules in all phases of planetary system formation -from molecular clouds to young stellar systems with protoplanetary disks -by measuring absorption spectra to determine the abundance and composition of ices toward > 2 × 10 4 Galactic targets. Interstellar ices are the likely source for water and organic molecules, the chemical basis of life on Earth, and knowledge of their abundance is key to understanding the formation of young planetary systems as well as the prospects for life on other planets.SPHEREx will chart the origin and history of galaxy formation through a deep survey mapping large-scale structure. This technique measures the total light produced by all galaxy populations, complementing studies based on deep galaxy counts, to trace the history of galactic light production from the present day to the first galaxies that ended the cosmic dark ages.SPHEREx will be the first all-sky near-infrared spectral survey, creating a legacy archive of spectra (0.75 ≤ λ ≤...

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