The next generation "Stage-4" ground-based cosmic microwave background (CMB) experiment, CMB-S4, consisting of dedicated telescopes equipped with highly sensitive superconducting cameras operating at the South Pole, the high Chilean Atacama plateau, and possibly northern hemisphere sites, will provide a dramatic leap forward in our understanding of the fundamental nature of space and time and the evolution of the Universe. CMB-S4 will be designed to cross critical thresholds in testing inflation, determining the number and masses of the neutrinos, constraining possible new light relic particles, providing precise constraints on the nature of dark energy, and testing general relativity on large scales.CMB-S4 is intended to be the definitive ground-based CMB project. It will deliver a highly constraining data set with which any model for the origin of the primordial fluctuations-be it inflation or an alternative theory-and their evolution to the structure seen in the Universe today must be consistent. While we have learned a great deal from CMB measurements, including discoveries that have pointed the way to new physics, we have only begun to tap the information encoded in CMB polarization, CMB lensing and other secondary effects. The discovery space from these and other yet to be imagined effects will be maximized by designing CMB-S4 to produce high-fidelity maps, which will also ensure enormous legacy value for CMB-S4. CMB-S4 is the logical successor to the Stage-3 CMB projects which will operate over the next few years. For maximum impact, CMB-S4 should be implemented on a schedule that allows a transition from Stage 3 to Stage 4 that is as seamless and as timely as possible, preserving the expertise in the community and ensuring a continued stream of CMB science results. This timing is also necessary to ensure the optimum synergistic enhancement of the science return from contemporaneous optical surveys (e.g., LSST, DESI, Euclid and WFIRST). Information learned from the ongoing Stage-3 experiments can be easily incorporated into CMB-S4 with little or no impact on its design. In particular, additional information on the properties of Galactic foregrounds would inform the detailed distribution of detectors among frequency bands in CMB-S4. The sensitivity and fidelity of the multiple band foreground measurements needed to realize the goals of CMB-S4 will be provided by CMB-S4 itself, at frequencies just below and above those of the main CMB channels. This timeline is possible because CMB-S4 will use proven existing technology that has been developed and demonstrated by the CMB experimental groups over the last decade. There are, to be sure, considerable technical challenges presented by the required scaling-up of the instrumentation and by the scope and complexity of the data analysis and interpretation. CMB-S4 will require: scaled-up superconducting detector arrays with well-understood and robust material properties and processing techniques; high-throughput mmwave telescopes and optics with unprecedented precisi...

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The detection of primordial non-Gaussianity could provide a powerful means to test various inflationary scenarios. Although scale-invariant non-Gaussianity (often described by the f N L formalism) is currently best constrained by the CMB, single-field models with changing sound speed can have strongly scale-dependent non-Gaussianity. Such models could evade the CMB constraints but still have important effects at scales responsible for the formation of cosmological objects such as clusters and galaxies. We compute the effect of scale-dependent primordial non-Gaussianity on cluster number counts as a function of redshift, using a simple ansatz to model scale-dependent features. We forecast constraints on these models achievable with forthcoming data sets. We also examine consequences for the galaxy bispectrum. Our results are relevant for the Dirac-Born-Infeld model of brane inflation, where the scale-dependence of the non-Gaussianity is directly related to the geometry of the extra dimensions.

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 develop a systematic derivation for the Limber approximation to the angular cross-power spectrum of two random fields, as a series expansion in (ℓ + 1/2) −1 . This extended Limber approximation can be used to test the accuracy of the Limber approximation and to improve the rate of convergence at large ℓ's. We show that the error in ordinary Limber approximation is O(ℓ −2 ). We also provide a simple expression for the 2 nd order correction to the Limber formula, which improves the accuracy to O(ℓ −4 ). This correction can be especially useful for narrow redshift bins, or samples with small redshift overlap, for which the 0 th order Limber formula has a large error. We also point out that using ℓ instead of ℓ + 1/2, as is often done in the literature, spoils the accuracy of the approximation to O(ℓ −1 ).

One of the primary scientific targets of current and future CMB polarization experiments is the search for a stochastic background of gravity waves in the early universe. As instrumental sensitivity improves, the limiting factor will eventually be B-mode power generated by gravitational lensing, which can be removed through use of so-called "delensing" algorithms. We forecast prospects for delensing using lensing maps which are obtained externally to CMB polarization: either from largescale structure observations, or from high-resolution maps of CMB temperature. We conclude that the forecasts in either case are not encouraging, and that significantly delensing large-scale CMB polarization requires high-resolution polarization maps with sufficient sensitivity to measure the lensing B-mode. We also present a simple formalism for including delensing in CMB forecasts which is computationally fast and agrees well with Monte Carlos.

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