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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In models of natural inflation, the inflaton is an axion-like particle. Unfortunately, axion potentials in UV-complete theories appear to be too steep to drive inflation. We show that, even for a steep potential, natural inflation can occur if the coupling between axion and gauge fields is taken into account. Due to this coupling, quanta of the gauge field are produced by the rolling of the axion. If the coupling is large enough, such a dissipative effect slows down the axion, leading to inflation even for a steep potential. The spectrum of perturbations is quasi-scale invariant, but in the simplest construction its amplitude is larger than 10 −5 . We discuss a possible way out of this problem.PACS numbers: 98.80.CqAxion-like particles are the simplest spin-zero degrees of freedom with a nontrivial radiatively stable potential. Moreover, they are abundant in string theory. As a consequence, axions provide excellent inflaton candidates in a UV complete theory that includes gravity. Inflation driven by axions was proposed as early as in 1990 as natural inflation [1]. The axion potential is radiatively stable thanks to a (broken) shift symmetry, and has the form V (Φ) = Λ 4 [cos(Φ/f ) + 1], where f is the axion constant. Neglecting all interactions of Φ apart from those in V (Φ) and those with gravity, the condition for inflation is that V (Φ) is flat in units of the Planck scale (i.e.,for a sufficiently wide range of Φ. In the case of the axion, these conditions are equivalent to f ≫ M P . Unfortunately, string theory appears not to allow such large values of f [2]. Moreover, f < ∼ M P appears also as a consequence of the "gravity as the weakest force" conjecture of [3].In this paper, we show that natural inflation can be realized also for a steep potential. Our mechanism relies on the coupling of the inflaton to gauge fields through the operator Φ F µνF µν . As Φ rolls down its potential, it provides a time-dependent background for the gauge field whose vacuum fluctuations are thus amplified into physical excitations. This production of quanta of gauge field occurs at the expenses of the kinetic energy of the inflaton, slowing it down. If the coupling between Φ and F µν is strong enough, such a dissipation effect can allow to obtain a sufficiently long period of inflation even if f ≪ M P . This way, the question of finding natural inflation in string theory is formulated in a new way: is there, among the many axions of string theory [4], one whose coupling to the gauge fields is large enough? We will argue in Appendix B that the answer to this question might be positive.

We show that inflation with a quadratic potential occurs naturally in theories where an axion-like field mixes with a 4-form. Such an axion is massive, with the mass which arises from the mixing being protected by the axion shift symmetry. The 4-form backgrounds break this symmetry spontaneously and comprise a mini-landscape, where their fluxes can change by emission of membranes. Inflation can begin when the 4-form dominates the energy density. Eventually this energy is reduced by membrane emission and the axion can roll slowly towards its minimum, as in the simplest version of chaotic inflation.

We study an inflationary model developed by Kaloper and Sorbo, in which the inflaton is an axion with a sub-Planckian decay constant, whose potential is generated by mixing with a topological 4-form field strength. This gives a 4d construction of "axion monodromy inflation": the axion winds many times over the course of inflation and draws energy from the 4-form. The classical theory is equivalent to chaotic inflation with a quadratic inflaton potential. Such models can produce "high scale" inflation driven by energy densities of the order of (10 16 GeV ) 4 , which produces primordial gravitational waves potentially accessible to CMB polarization experiments. We analyze the possible corrections to this scenario from the standpoint of 4d effective field theory, identifying the physics which potentially suppresses dangerous corrections to the slow-roll potential. This yields a constraint relation between the axion decay constant, the inflaton mass, and the 4-form charge. We show how these models can evade the fundamental constraints which typically make high-scale inflation difficult to realize. Specifically, the moduli coupling to the axion-four-form sector must have masses higher than the inflationary Hubble scale ( < ∼ 10 14 GeV ). There are also constraints from states that become light due to multiple windings of the axion, as happens in explicit string theory constructions of this scenario. Further, such models generally have a quantum-mechanical "tunneling mode" in which the axion jumps between windings, which must be suppressed. Finally, we outline possible observational signatures.