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We measure the mass function of dark matter halos in a large set of collisionless cosmological simulations of flat ΛCDM cosmology and investigate its evolution at z 2. Halos are identified as isolated density peaks, and their masses are measured within a series of radii enclosing specific overdensities. We argue that these spherical overdensity masses are more directly linked to cluster observables than masses measured using the friends-of-friends algorithm (FOF), and are therefore preferable for accurate forecasts of halo abundances. Our simulation set allows us to calibrate the mass function at z = 0 for virial masses in the range 10 11 h −1 M ⊙ ≤ M ≤ 10 15 h −1 M ⊙ to 5%. We derive fitting functions for the halo mass function in this mass range for a wide range of overdensities, both at z = 0 and earlier epochs. In addition to these formulae, which improve on previous approximations by 10-20%, our main finding is that the mass function cannot be represented by a universal fitting function at this level of accuracy. The amplitude of the "universal" function decreases monotonically by ≈ 20 − 50%, depending on the mass definition, from z = 0 to 2.5. We also find evidence for redshift evolution in the overall shape of the mass function. Subject headings: cosmology:theory -dark matter:halos -methods:numerical -large scale structure of the universe

We measure cosmological parameters using the three-dimensional power spectrum P (k) from over 200,000 galaxies in the Sloan Digital Sky Survey (SDSS) in combination with WMAP and other data. Our results are consistent with a "vanilla" flat adiabatic ΛCDM model without tilt (ns = 1), running tilt, tensor modes or massive neutrinos. Adding SDSS information more than halves the WMAP-only error bars on some parameters, tightening 1σ constraints on the Hubble parameter from h ≈ 0.74−0.03 , on the matter density from Ωm ≈ 0.25 ± 0.10 to Ωm ≈ 0.30 ± 0.04 (1σ) and on neutrino masses from < 11 eV to < 0.6 eV (95%). SDSS helps even more when dropping prior assumptions about curvature, neutrinos, tensor modes and the equation of state. Our results are in substantial agreement with the joint analysis of WMAP and the 2dF Galaxy Redshift Survey, which is an impressive consistency check with independent redshift survey data and analysis techniques. In this paper, we place particular emphasis on clarifying the physical origin of the constraints, i.e., what we do and do not know when using different data sets and prior assumptions. For instance, dropping the assumption that space is perfectly flat, the WMAP-only constraint on the measured age of the Universe tightens from t0 ≈ 16.3 +2.3 −1.8 Gyr to t0 ≈ 14.1Gyr by adding SDSS and SN Ia data. Including tensors, running tilt, neutrino mass and equation of state in the list of free parameters, many constraints are still quite weak, but future cosmological measurements from SDSS and other sources should allow these to be substantially tightened.

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...

We measure the large-scale real-space power spectrum P (k) using luminous red galaxies (LRGs) in the Sloan Digital Sky Survey (SDSS) and use this measurement to sharpen constraints on cosmological parameters from the Wilkinson Microwave Anisotropy Probe (WMAP). We employ a matrix-based power spectrum estimation method using Pseudo-Karhunen-Loève eigenmodes, producing uncorrelated minimum-variance measurements in 20 k-bands of both the clustering power and its anisotropy due to redshift-space distortions, with narrow and well-behaved window functions in the range 0.01 h/Mpc < k < 0.2 h/Mpc. Results from the LRG and main galaxy samples are consistent, with the former providing higher signal-to-noise. Our results are robust to omitting angular and radial density fluctuations and are consistent between different parts of the sky. They provide a striking confirmation of the predicted large-scale ΛCDM power spectrum. Combining only SDSS LRG and WMAP data places robust constraints on many cosmological parameters that complement prior analyses of multiple data sets. The LRGs provide independent cross-checks on Ωm and the baryon fraction in good agreement with WMAP. Within the context of flat ΛCDM models, our LRG measurements complement WMAP by sharpening the constraints on the matter density, the neutrino density and the tensor amplitude by about a factor of two, giving Ωm = 0.24±0.02 (1σ), mν ∼ < 0.9 eV (95%) and r < 0.3 (95%). Baryon oscillations are clearly detected and provide a robust measurement of the comoving distance to the median survey redshift z = 0.35 independent of curvature and dark energy properties. Within the ΛCDM framework, our power spectrum measurement improves the evidence for spatial flatness, sharpening the curvature constraint Ωtot = 1.05±0.05 from WMAP alone to Ωtot = 1.003 ± 0.010. Assuming Ωtot = 1, the equation of state parameter is constrained to w = −0.94 ± 0.09, indicating the potential for more ambitious future LRG measurements to provide precision tests of the nature of dark energy. All these constraints are essentially independent of scales k > 0.1h/Mpc and associated nonlinear complications, yet agree well with more aggressive published analyses where nonlinear modeling is crucial. k [h/Mpc] Power Pg 0.012 +0.005 −0.004 124884 ± 18775 0.015 +0.003 −0.002 118814 ± 29400 0.018 +0.004 −0.002 134291 ± 21638 0.021 +0.004 −0.003 58644 ± 16647 0.024 +0.004 −0.003 105253 ± 12736 0.028 +0.005 −0.003 77699 ± 9666 0.032 +0.005 −0.003 57870 ± 7264 0.037 +0.006 −0.004 56516 ± 5466 0.043 +0.008 −0.006 50125 ± 3991 0.049 +0.008 −0.007 45076 ± 2956 0.057 +0.009 −0.007 39339 ± 2214 0.065 +0.010 −0.008 39609 ± 1679 0.075 +0.011 −0.009 31566 ± 1284 0.087 +0.