Science Book
The purpose of Science Book is to set the scientific goals for CMB-S4 and specify the measurements needed to achieve them, which will then be translated into the instrument requirements. This will set the stage for defining the instrument.

This Science Book is the product of a large, global community of scientists who are united in support of proceeding with CMB-S4, which will make key advances in our understanding of the fundamental nature of space and time and the evolution of the Universe.CMB-S4 Science Book, First Edition

Executive Summary
The evolution of the raw sensitivity of CMB experiments

Plot illustrating the evolution of the raw sensitivity of CMB experiments, which scales as the total number of bolometers. Ground-based CMB experiments are classified into Stages with Stage II experiments having O (1000) detectors, Stage III experiments having O (10,000) detectors, and a Stage IV experiment (such as CMB-S4) having O (100,000) detectors. Figure from Snowmass CF5 Neutrino planning document.
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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.

investigating the origin of primordial perturbations and the beginning of time
Inflation, a period of accelerated expansion of the early Universe, is the leading paradigm for explaining the origin of the primordial density perturbations that grew into the CMB anisotropies and eventually into the stars and galaxies we see around us. In addition to primordial density perturbations, the rapid expansion creates primordial gravitational waves that imprint a characteristic polarization pattern onto the CMB. If our Universe is described by a typical model of inflation that naturally explains the statistical properties of the density perturbations, CMB-S4 will detect this signature of inflation. A detection of this particular polarization pattern would open a completely new window onto the physics of the early Universe and provide us with an additional relic left over from the hot big bang. This relic would constitute our most direct probe of the very early Universe and transform our understanding of several aspects of fundamental physics. Because the polarization pattern is due to quantum fluctuations in the gravitational field during inflation, it would provide insights into the quantum nature of gravity. The strength of the signal, encoded in the tensor-to-scalar ratio r, would provide a direct measurement of the expansion rate of the Universe during inflation. A detection with CMB-S4 would point to inflationary physics near the energy scale associated with grand uni ed theories and would provide additional evidence in favor of the idea of the uni cation of forces. Knowledge of the scale of inflation would also have broad implications for many other aspects of fundamental physics, including ubiquitous ingredients of string theory like axions and moduli.

Even an upper limit of r < 0.002 at 95% CL achievable by CMB-S4, over an order of magnitude stronger than current limits, would significantly advance our understanding of inflation. It would rule out the most popular and most widely studied classes of models and dramatically impact how we think about the theory. To some, the remaining class of models would be contrived enough to give up on inflation altogether. Furthermore, CMB-S4 is in a unique position to probe the statistical properties of primordial density perturbations through measurements of primary anisotropies in the temperature and polarization of the CMB with unprecedented precision, providing us with invaluable information about the early Universe.

setting the neutrino mass scale and testing the 3-neutrino paradigm
The effect of massive neutrinos on the matter power spectrum and CMB lensing power spectrum. Top Left: The effect of neutrino mass on the matter power spectrum. Top Right: The change to the matter power spectrum relative to the case with massless neutrinos. Bottom Left: The projected matter power spectrum observed through CMB lensing shows the same suppression with neutrino mass. Bottom Right: The relative change to the lensing potential power spectrum.
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Neutrinos are the least explored corner of the Standard Model of particle physics. The 2015 Nobel Prize recognized the discovery of neutrino oscillations, which shows that they have mass. However, the overall scale of the masses and the full suite of mixing parameters are still not measured. Cosmology offers a unique view of neutrinos; they were produced in large numbers in the high temperatures of the early universe and left a distinctive imprint in the cosmic microwave background and on the large-scale structure of the universe. Therefore, CMB-S4 and large-scale structure surveys together will have the power to detect properties of neutrinos that supplement those probed by large terrestrial experiments such as short- and long-baseline as well as neutrino-less double beta decay experiments.

Light Relics
searching for new light particles
New light particles appear in many attempts to understand both the observed laws of physics and extensions to higher energies. These light particles are often deeply tied to the underlying symmetries of nature and can play crucial roles in understanding some of the great outstanding problems in physics. In most cases, these particles interact too weakly to be produced at an appreciable level in Earth-based experiments, making them experimentally elusive. At the very high temperatures believed to be present in the early Universe, however, even extremely weakly coupled particles can be produced prolifically and can reach thermal equilibrium with the Standard Model particles. Light particles (masses less than 0.1 eV) produced at early times survive until the time when the CMB is emitted and direct observations become possible. Neutrinos are one example of such a relic found in the Standard Model. Extensions of the Standard Model also include a wide variety of possible light relics including axions, sterile neutrinos, hidden photons, and gravitinos. As a result, the search for light relics from the early Universe with CMB-S4 can shed light on some of the most important questions in fundamental physics, complementing existing collider searches and e orts to detect these light particles in the lab.

Dark Matter
searching for heavy WIMPS and extremely light axions
Dark matter is required to explain a host of cosmological observations such as the velocities of galaxies in galaxy clusters, galaxy rotation curves, strong and weak lensing measurements, and the acoustic peak structure of the CMB. While most of these observations could be explained by non-luminous baryonic matter, the CMB provides overwhelming evidence that 85% of the matter in the Universe is non-baryonic, presumably a new particle never observed in terrestrial experiments. Because dark matter has only been observed through its gravitational effects, its microscopic properties remain a mystery. Identifying its nature and its connection to the rest of physics is one of the prime challenges of high energy physics

Dark Energy
measuring cosmic acceleration and testing general relativity
The discovery almost 20 years ago that the expansion of the universe is accelerating presented a profound challenge to our laws of physics, one that we have yet to conquer. Our current framework can explain these observations only by invoking a new substance with bizarre properties (dark energy) or by changing the century-old, well-tested theory of general relativity invented by Einstein. The current epoch of acceleration is much later than the epoch from which the photons in the CMB originate, and the behavior of dark energy or modifications of gravity do not significantly influence the properties of the primordial CMB. However, during their long journey to our telescopes, CMB photons occasionally interact with the intervening matter and can have their trajectories and their energies slightly distorted. These distortions -- gravitational lensing by intervening mass and energy gain by scattering o hot electrons -- are small, but powerful experiments currently online have already detected them, and CMB-S4 will exploit them to the fullest extent, enabling us to learn about the mechanism driving the current epoch of acceleration

CMB lensing
mapping all the mass in the Universe
The distribution of matter in the Universe contains a wealth of information about the primordial density perturbations and the forces that have shaped our cosmological evolution. Mapping this distribution is one of the central goals of modern cosmology. Gravitational lensing provides a unique method to map the matter between us and distant light sources, and lensing of the CMB, the most distant light source available, allows us to map the matter between us and the surface of last scattering.

Data Analysis, Simulations & Forecasting
Extracting science from a CMB dataset is a complex, iterative process requiring expertise in both physical and computational sciences. An integral part of the analysis process is played by high-fidelity simulations of the millimeter-wave sky and the experiment's response to the various sources of emission. Fast-turnaround versions of these sky and instrument simulations play a key role at the instrument design stage, allowing exploration of instrument configuration parameter space and projections for science yield. In all three of these areas (analysis, simulations, forecasting), the large leap in detector count and complexity of CMB- S4 over fielded experiments presents challenges to current methods. Some of these challenges are purely computational -- for example, performing full time-ordered-data simulations for CMB-S4 will require computing resources and distributed computing tools significantly beyond what was required for Planck. Other challenges are algorithmic, including finding the optimal way to separate the CMB signal of interest from foregrounds and how to optimally combine data from different experimental platforms. To meet these challenges, we will bring the full intellectual and technical resources of the CMB community to bear, in an effort analogous to the uni ed effort among hardware groups to build the CMB-S4 instrument. A wide cross-section of the CMB theory, phenomenology, and analysis communities has already come together to produce the forecasts shown elsewhere in this document, including detailed code comparisons and agreement on unified frameworks for forecasting.