This document on the CMB-S4 Science Case, Reference Design, and Project Plan is the product of a global community of scientists who are united in support of advancing CMB-S4 to cross key thresholds in our understanding of the fundamental nature of space and time and the evolution of the Universe. CMB-S4 is planned to be a joint National Science Foundation (NSF) and Department of Energy (DOE) project, with the construction phase to be funded as an NSF Major Research Equipment and Facilities Construction (MREFC) project and a DOE High Energy Physics (HEP) Major Item of Equipment (MIE) project. At the time of this writing, an interim project office has been constituted and tasked with advancing the CMB-S4 project in the NSF MREFC Preliminary Design Phase and toward DOE Critical Decision CD-1. DOE CD-0 is expected imminently.CMB-S4 has been in development for six years. Through the Snowmass Cosmic Frontier planning process, experimental groups in the cosmic microwave background (CMB) and broader cosmology communities came together to produce two influential CMB planning papers, endorsed by over 90 scientists, that outlined the science case as well as the CMB-S4 instrumental concept [1, 2]. It immediately became clear that an enormous increase in the scale of ground-based CMB experiments would be needed to achieve the exciting thresholdcrossing scientific goals, necessitating a phase change in the ground-based CMB experimental program. To realize CMB-S4, a partnership of the university-based CMB groups, the broader cosmology community, and the national laboratories would be needed.The community proposed CMB-S4 to the 2014 Particle Physics Project Prioritization Process (P5) as a single, community-wide experiment, jointly supported by DOE and NSF. Following P5's recommendation of CMB-S4 under all budget scenarios, the CMB community started in early 2015 to hold biannual workshops -open to CMB scientists from around the world -to develop and refine the concept. Nine workshops have been held to date, typically with 150 to 200 participants. The workshops have focused on developing the unique and vital role of the future ground-based CMB program. This growing CMB-S4 community produced a detailed and influential CMB-S4 Science Book [3] and a CMB-S4 Technology Book [4]. Over 200 scientists contributed to these documents. These and numerous other reports, workshop and working group wiki pages, email lists, and much more may be found at the website http://CMB-S4.org.Soon after the CMB-S4 Science Book was completed in August 2016, DOE and NSF requested the Astronomy and Astrophysics Advisory Committee (AAAC) to convene a Concept Definition Taskforce (CDT) to conduct a CMB-S4 concept study. The resulting report was unanimously accepted in late 2017. 1 One recommendation of the CDT report was that the community should organize itself into a formal collaboration. An Interim Collaboration Coordination Committee was elected by the community to coordinate this process. The resulting draft bylaws were refined at the Spring 2018 CMB-S4...

We present a precise estimate of the bulk virial scaling relation of halos formed via hierarchical clustering in an ensemble of simulated cold dark matter cosmologies. The result is insensitive to cosmological parameters, the presence of a trace, dissipationless gas component, and numerical resolution down to a limit of ∼ 1000 particles. The dark matter velocity dispersion scales with total mass as log(σ DM (M, z)) = log(1082.9 ± 4.0 km s −1 ) + (0.3361 ± 0.0026) log(h(z)M 200 /10 15 M ⊙ ), with h(z) the dimensionless Hubble parameter. At fixed mass, the velocity dispersion likelihood is nearly log-normal, with scatter σ ln σ = 0.0426 ± 0.015, except for a tail to higher dispersions containing 10% of the population that are merger transients. We combine this relation with the halo mass function in ΛCDM models, and show that a low normalization condition, S 8 = σ 8 (Ω m /0.3) 0.35 = 0.69, favored by recent WMAP and SDSS analysis requires that galaxy and gas specific energies in rich clusters be 50% larger than that of the underlying dark matter. Such large energetic biases are in conflict with the current generation of direct simulations of cluster formation. A higher normalization, S 8 = 0.80, alleviates this tension and implies that the hot gas fraction within r 500 is (0.71 ± 0.09)h −3/2 70 Ω b /Ω m , a value consistent with recent Sunyaev-Zel'dovich observations.

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 ≤...

Near-future cosmological observations targeted at investigations of dark energy pose stringent requirements on the accuracy of theoretical predictions for the nonlinear clustering of matter. Currently, N-body simulations comprise the only viable approach to this problem. In this paper we study various sources of computational error and methods to control them. By applying our methodology to a large suite of cosmological simulations we show that results for the (gravity-only) nonlinear matter power spectrum can be obtained at 1% accuracy out to k ∼ 1 h Mpc −1 . The key components of these high accuracy simulations are: precise initial conditions, very large simulation volumes, sufficient mass resolution, and accurate time stepping. This paper is the first in a series of three; the final aim is a high-accuracy prediction scheme for the nonlinear matter power spectrum that improves current fitting formulae by an order of magnitude. Subject headings: methods: N-body simulations -cosmology: large-scale structure of universe 1

Modern sky surveys are returning precision measurements of cosmological statistics such as weak lensing shear correlations, the distribution of galaxies, and cluster abundance. To fully exploit these observations, theorists must provide predictions that are at least as accurate as the measurements, as well as robust estimates of systematic errors that are inherent to the modeling process. In the nonlinear regime of structure formation, this challenge can only be overcome by developing a large-scale, multi-physics simulation capability covering a range of cosmological models and astrophysical processes. As a first step to achieving this goal, we have recently developed a prediction scheme for the matter power spectrum (a so-called emulator), accurate at the 1% level out to k ∼ 1 Mpc −1 and z = 1 for wCDM cosmologies based on a set of high-accuracy N-body simulations. It is highly desirable to increase the range in both redshift and wavenumber and to extend the reach in cosmological parameter space. To make progress in this direction, while minimizing computational cost, we present a strategy that maximally reuses the original simulations. We demonstrate improvement over the original spatial dynamic range by an order of magnitude, reaching k ∼ 10 h Mpc −1 , a four-fold increase in redshift coverage, to z = 4, and now include the Hubble parameter as a new independent variable. To further the range in k and z, a new set of nested simulations run at modest cost is added to the original set. The extension in h is performed by including perturbation theory results within a multi-scale procedure for building the emulator. This economical methodology still gives excellent error control, ∼5% near the edges of the domain of applicability of the emulator. A public domain code for the new emulator is released as part of the work presented in this paper.

Dark matter-dominated cluster-scale halos act as an important cosmological probe and provide a key testing ground for structure formation theory. Focusing on their mass profiles, we have carried out (gravity-only) simulations of the concordance ΛCDM cosmology, covering a mass range of 2 × 10 12 − 2 × 10 15 h −1 M ⊙ and a redshift range of z = 0 − 2, while satisfying the associated requirements of resolution and statistical control. When fitting to the Navarro-Frenk-White profile, our concentration-mass (c − M) relation differs in normalization and shape in comparison to previous studies that have limited statistics in the upper end of the mass range. We show that the flattening of the c − M relation with redshift is naturally expressed if c is viewed as a function of the peak height parameter, ν. Unlike the c − M relation, the slope of the c − ν relation is effectively constant over the redshift range z = 0 − 2, while the amplitude varies by ∼ 30% for massive clusters. This relation is, however, not universal: Using a simulation suite covering the allowed wCDM parameter space, we show that the c − ν relation varies by about ± 20% as cosmological parameters are varied. At fixed mass, the c(M) distribution is well-fit by a Gaussian with σ c / c ≃ 0.33, independent of the radius at which the concentration is defined, the halo dynamical state, and the underlying cosmology. We compare the ΛCDM predictions with observations of halo concentrations from strong lensing, weak lensing, galaxy kinematics, and X-ray data, finding good agreement for massive clusters (M vir > 4 × 10 14 h −1 M ⊙ ), but with some disagreements at lower masses. Because of uncertainty in observational systematics and modeling of baryonic physics, the significance of these discrepancies remains unclear.

We study the formation of dark matter halos in the concordance ΛCDM model over a wide range of redshifts, from z = 20 to the present. Our primary focus is the halo mass function, a key probe of cosmology. By performing a large suite of nested-box N-body simulations with careful convergence and error controls (60 simulations with box sizes from 4 to 256 h −1 Mpc), we determine the mass function and its evolution with excellent statistical and systematic errors, reaching a few percent over most of the considered redshift and mass range. Across the studied redshifts, the halo mass is probed over 6 orders of magnitude (10 7 -10 13.5 h −1 M ⊙ ). Historically, there has been considerable variation in the high redshift mass function as obtained by different groups. We have made a concerted effort to identify and correct possible systematic errors in computing the mass function at high-redshift and to explain the discrepancies between some of the previous results. We discuss convergence criteria for the required force resolution, simulation box size, halo mass range, initial and final redshifts, and time stepping. Because of conservative cuts on the mass range probed by individual boxes, our results are relatively insensitive to simulation volume, the remaining sensitivity being consistent with extended Press-Schechter theory. Previously obtained mass function fits near z = 0, when scaled by linear theory, are in good agreement with our results at all redshifts, although a mild redshift dependence consistent with that found by Reed et al. may exist at low redshifts. Overall, our results are consistent with a "universal" form for the mass function at high redshifts.

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