Cosmic Discordance: Are Planck CMB and CFHTLenS weak lensing measurements out of tune?

We examine the level of agreement between low redshift weak lensing data and the CMB using measurements from the CFHTLenS and Planck+WMAP polarization. We perform an independent analysis of the CFHTLenS six bin tomography results of Heymans et al. (2013). We extend their systematics treatment and find the cosmological constraints to be relatively robust to the choice of non-linear modeling, extension to the intrinsic alignment model and inclusion of baryons. We find that the 90% confidence contours of CFHTLenS and Planck+WP do not overlap even in the full 6-dimensional parameter space of $\Lambda$CDM, so the two datasets are discrepant. Allowing a massive active neutrino or tensor modes does not significantly resolve the disagreement in the full n-dimensional parameter space. Our results differ from some in the literature because we use the full tomographic information in the weak lensing data and marginalize over systematics. We note that adding a sterile neutrino to $\Lambda$CDM does bring the 8-dimensional 64% contours to overlap, mainly due to the extra effective number of neutrino species, which we find to be 0.84 $\pm$ 0.35 (68%) greater than standard on combining the datasets. We discuss why this is not a completely satisfactory resolution, leaving open the possibility of other new physics or observational systematics as contributing factors. We provide updated cosmology fitting functions for the CFHTLenS constraints and discuss the differences from ones used in the literature.Comment: 12 pages, 8 figures. We compare our findings with studies that include other low redshift probes of structure. An interactive figure is available at http://bit.ly/1oZH0KQ. This version is that accepted by MNRAS, and so includes changes based on the referee's comments, and updates to the analysis cod

The Dark Side of Galaxy Color: evidence from new SDSS measurements of galaxy clustering and lensing

The age matching model has recently been shown to predict correctly the luminosity L and g-r color of galaxies residing within dark matter halos. The central tenet of the model is intuitive: older halos tend to host galaxies with older stellar populations. In this paper, we demonstrate that age matching also correctly predicts the g-r color trends exhibited in a wide variety of statistics of the galaxy distribution for stellar mass M* threshold samples. In particular, we present new measurements of the galaxy two-point correlation function and the galaxy-galaxy lensing signal as a function of M* and g-r color from the Sloan Digital Sky Survey, and show that age matching exhibits remarkable agreement with these and other statistics of low-redshift galaxies. In so doing, we also demonstrate good agreement between the galaxy-galaxy lensing observed by SDSS and the signal predicted by abundance matching, a new success of this model. We describe how age matching is a specific example of a larger class of Conditional Abundance Matching models (CAM), a theoretical framework we introduce here for the first time. CAM provides a general formalism to study correlations at fixed mass between any galaxy property and any halo property. The striking success of our simple implementation of CAM provides compelling evidence that this technique has the potential to describe the same set of data as alternative models, but with a dramatic reduction in the required number of parameters. CAM achieves this reduction by exploiting the capability of contemporary N-body simulations to determine dark matter halo properties other than mass alone, which distinguishes our model from conventional approaches to the galaxy-halo connection.Comment: references added, minor adjustments to text and notatio

A Redefinition of the Halo Boundary Leads to a Simple yet Accurate Halo Model of Large Scale Structure

We present a model for the halo--mass correlation function that explicitly incorporates halo exclusion. We assume that halos trace mass in a way that can be described using a single scale-independent bias parameter. However, our model exhibits scale dependent biasing due to the impact of halo-exclusion, the use of a ``soft'' (i.e. not infinitely sharp) halo boundary, and differences in the one halo term contributions to $\xi_{\rm hm}$ and $\xi_{\rm mm}$. These features naturally lead us to a redefinition of the halo boundary that lies at the ``by eye'' transition radius from the one--halo to the two--halo term in the halo--mass correlation function. When adopting our proposed definition, our model succeeds in describing the halo--mass correlation function with $\approx 2\%$ residuals over the radial range $0.1\ h^{-1}{\rm Mpc} < r < 80\ h^{-1}{\rm Mpc}$, and for halo masses in the range $10^{13}\ h^{-1}{\rm M}_{\odot} < M < 10^{15}\ h^{-1}{\rm M}_{\odot}$. Our proposed halo boundary is related to the splashback radius by a roughly constant multiplicative factor. Taking the 87-percentile as reference we find $r_{\rm t}/R_{\rm sp} \approx 1.3$. Surprisingly, our proposed definition results in halo abundances that are well described by the Press-Schechter mass function with $\delta_{\rm sc}=1.449\pm 0.004$. The clustering bias parameter is offset from the standard background-split prediction by $\approx 10\%-15\%$. This level of agreement is comparable to that achieved with more standard halo definitions.Comment: 12 pages, 5 figure

The Aemulus Project III: Emulation of the Galaxy Correlation Function

Using the N-body simulations of the AEMULUS Project, we construct an emulator for the non-linear clustering of galaxies in real and redshift space. We construct our model of galaxy bias using the halo occupation framework, accounting for possible velocity bias. The model includes 15 parameters, including both cosmological and galaxy bias parameters. We demonstrate that our emulator achieves ~ 1% precision at the scales of interest, 0.1<r<10 h^{-1} Mpc, and recovers the true cosmology when tested against independent simulations. Our primary parameters of interest are related to the growth rate of structure, f, and its degenerate combination fsigma_8. Using this emulator, we show that the constraining power on these parameters monotonically increases as smaller scales are included in the analysis, all the way down to 0.1 h^{-1} Mpc. For a BOSS-like survey, the constraints on fsigma_8 from r<30 h^{-1} Mpc scales alone are more than a factor of two tighter than those from the fiducial BOSS analysis of redshift-space clustering using perturbation theory at larger scales. The combination of real- and redshift-space clustering allows us to break the degeneracy between f and sigma_8, yielding a 9% constraint on f alone for a BOSS-like analysis. The current AEMULUS simulations limit this model to surveys of massive galaxies. Future simulations will allow this framework to be extended to all galaxy target types, including emission-line galaxies.Comment: 14 pages, 8 figures, 1 table; submitted to ApJ; the project webpage is available at https://aemulusproject.github.io ; typo in Figure 7 and caption updated, results unchange

The Aemulus Project I: Numerical Simulations for Precision Cosmology

The rapidly growing statistical precision of galaxy surveys has lead to a need for ever-more precise predictions of the observables used to constrain cosmological and galaxy formation models. The primary avenue through which such predictions will be obtained is suites of numerical simulations. These simulations must span the relevant model parameter spaces, be large enough to obtain the precision demanded by upcoming data, and be thoroughly validated in order to ensure accuracy. In this paper we present one such suite of simulations, forming the basis for the AEMULUS Project, a collaboration devoted to precision emulation of galaxy survey observables. We have run a set of 75 (1.05 h^-1 Gpc)^3 simulations with mass resolution and force softening of 3.51\times 10^10 (Omega_m / 0.3) ~ h^-1 M_sun and 20 ~ h^-1 kpc respectively in 47 different wCDM cosmologies spanning the range of parameter space allowed by the combination of recent Cosmic Microwave Background, Baryon Acoustic Oscillation and Type Ia Supernovae results. We present convergence tests of several observables including spherical overdensity halo mass functions, galaxy projected correlation functions, galaxy clustering in redshift space, and matter and halo correlation functions and power spectra. We show that these statistics are converged to 1% (2%) for halos with more than 500 (200) particles respectively and scales of r>200 ~ h^-1 kpc in real space or k ~ 3 h Mpc^-1 in harmonic space for z\le 1. We find that the dominant source of uncertainty comes from varying the particle loading of the simulations. This leads to large systematic errors for statistics using halos with fewer than 200 particles and scales smaller than k ~ 4 h^-1 Mpc. We provide the halo catalogs and snapshots detailed in this work to the community at https://AemulusProject.github.io.Comment: 16 pages, 12 figures, 3 Tables Project website: https://aemulusproject.github.io