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 present cosmological results from the final galaxy clustering data set of the Baryon Oscillation Spectroscopic Survey, part of the Sloan Digital Sky Survey III. Our combined galaxy sample comprises 1.2 million massive galaxies over an effective area of 9329 deg 2 and volume of 18.7 Gpc 3 , divided into three partially overlapping redshift slices centred at effective redshifts 0.38, 0.51 and 0.61. We measure the angular diameter distance D M and Hubble parameter H from the baryon acoustic oscillation (BAO) method, in combination with a cosmic microwave background prior on the sound horizon scale, after applying reconstruction to reduce non-linear effects on the BAO feature. Using the anisotropic clustering of the Hubble Fellow.

We measure the clustering of dark matter halos in a large set of collisionless cosmological simulations of the flat ΛCDM cosmology. Halos are identified using the spherical overdensity algorithm, which finds the mass around isolated peaks in the density field such that the mean density is Δ times the background. We calibrate fitting functions for the large-scale bias that are adaptable to any value of Δ we examine. We find a ∼6% scatter about our best-fit bias relation. Our fitting functions couple to the halo mass functions of Tinker et al. such that the bias of all dark matter is normalized to unity. We demonstrate that the bias of massive, rare halos is higher than that predicted in the modified ellipsoidal collapse model of Sheth et al. and approaches the predictions of the spherical collapse model for the rarest halos. Halo bias results based on friends-of-friends halos identified with linking length 0.2 are systematically lower than for halos with the canonical Δ = 200 overdensity by ∼10%. In contrast to our previous results on the mass function, we find that the universal bias function evolves very weakly with redshift, if at all. We use our numerical results, both for the mass function and the bias relation, to test the peak-background split model for halo bias. We find that the peak-background split achieves a reasonable agreement with the numerical results, but ∼20% residuals remain, both at high and low masses.

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