The Coyote Universe I: Precision Determination of the Nonlinear Matter Power Spectrum

Near-future cosmological observations targeted at investigations of dark energy pose stringent requirements on the accuracy of theoretical predictions for the clustering of matter. Currently, N-body simulations comprise the only viable approach to this problem. In this paper we demonstrate that N-body simulations can indeed be sufficiently controlled to fulfill these requirements for the needs of ongoing and near-future weak lensing surveys. By performing a large suite of cosmological simulation comparison and convergence tests we show that results for the nonlinear matter power spectrum can be obtained at 1% accuracy out to k~1 h/Mpc. The key components of these high accuracy simulations are: precise initial conditions, very large simulation volumes, sufficient mass resolution, and accurate time stepping. This paper is the first in a series of three, with the final aim to provide a high-accuracy prediction scheme for the nonlinear matter power spectrum.Comment: 18 pages, 22 figures, minor changes to address referee repor

Nonequilibrium evolution and symmetry structure of the large-N Φ4\Phi^4 model at finite temperature

We consider the large-N $\Phi^4$ theory with spontaneously broken symmetry at finite temperature. We study, in the large-N limit, quantum states which are characterized by a time dependent, spatially homogenous expectation value of one of the field components, $\phi_N(t)$, and by quantum fluctuations of the other $N-1$ components, that evolve in the background of the classical field. Investigating such systems out of equilibrium has recently been shown to display several interesting features. We extend here this type of investigations to finite temperature systems. Essentially the novel features observed at T=0 carry over to finite temperature. This is not unexpected, as the main mechanisms that determine the late-time behavior remain the same. We extend two empirical - presumably exact - relations for the late-time behavior to finite temperature and use them to define the boundaries between the region of different asymptotic regimes. This results in a phase diagram with the temperature and the initial value of the classical field as parameters, the phases being characterized by spontaneous symmetry breaking resp. symmetry restoration. The time evolution is computed numerically and agrees very well with the expectations.Comment: 21 pages, 13 Figures, LaTeX, some typos correcte

Mass Function Predictions Beyond LCDM

The mass distribution of halos, as specified by the halo mass function, is a key input for several cosmological probes. The sizes of $N$-body simulations are now such that, for the most part, results need no longer be statistics-limited, but are still subject to various systematic uncertainties. We investigate and discuss some of the reasons for these differences. Quantifying error sources and compensating for them as appropriate, we carry out a high-statistics study of dark matter halos from 67 $N$-body simulations to investigate the mass function and its evolution for a reference $\Lambda$CDM cosmology and for a set of $w$CDM cosmologies. For the reference $\Lambda$CDM cosmology (close to WMAP5), we quantify the breaking of universality in the form of the mass function as a function of redshift, finding an evolution of as much as 10% away from the universal form between redshifts $z=0$ and $z=2$. For cosmologies very close to this reference we provide a fitting formula to our results for the (evolving) $\Lambda$CDM mass function over a mass range of $6\cdot 10^{11}-3\cdot 10^{15}$ M$_{\odot}$ to an estimated accuracy of about 2%. The set of $w$CDM cosmologies is taken from the Coyote Universe simulation suite. The mass functions from this suite (which includes a $\Lambda$CDM cosmology and others with $w\simeq-1$) are described by the fitting formula for the reference $\Lambda$CDM case at an accuracy level of 10%, but with clear systematic deviations. We argue that, as a consequence, fitting formulae based on a universal form for the mass function may have limited utility in high precision cosmological applications.Comment: 19 pages; 18 figures; accepted for publication in the Ap

Analyzing and Visualizing Cosmological Simulations with ParaView

The advent of large cosmological sky surveys - ushering in the era of precision cosmology - has been accompanied by ever larger cosmological simulations. The analysis of these simulations, which currently encompass tens of billions of particles and up to trillion particles in the near future, is often as daunting as carrying out the simulations in the first place. Therefore, the development of very efficient analysis tools combining qualitative and quantitative capabilities is a matter of some urgency. In this paper we introduce new analysis features implemented within ParaView, a parallel, open-source visualization toolkit, to analyze large N-body simulations. The new features include particle readers and a very efficient halo finder which identifies friends-of-friends halos and determines common halo properties. In combination with many other functionalities already existing within ParaView, such as histogram routines or interfaces to Python, this enhanced version enables fast, interactive, and convenient analyses of large cosmological simulations. In addition, development paths are available for future extensions.Comment: 9 pages, 8 figure

Removable Matter-Power-Spectrum Covariance from Bias Fluctuations

We find a simple, accurate model for the covariance matrix of the real-space cosmological matter power spectrum on slightly nonlinear scales (k~0.1-0.8 h/Mpc at z=0), where off-diagonal matrix elements become substantial. The model includes a multiplicative, scale-independent modulation of the power spectrum. It has only one parameter, the variance (among realizations) of the variance of the nonlinear density field in cells, with little dependence on the cell size between 2-8 Mpc/h. Furthermore, we find that this extra covariance can be modeled out by instead measuring the power spectrum of (delta/sigma_cell), i.e. the ratio of the overdensity to its dispersion in cells a few Mpc in size. Dividing delta by sigma_cell essentially removes the non-Gaussian part of the covariance matrix, nearly diagonalizing it.Comment: Accepted to ApJ. 5 pages, 5 figures; slight clarifications to match accepted versio

The Coyote Universe III: Simulation Suite and Precision Emulator for the Nonlinear Matter Power Spectrum

Many of the most exciting questions in astrophysics and cosmology, including the majority of observational probes of dark energy, rely on an understanding of the nonlinear regime of structure formation. In order to fully exploit the information available from this regime and to extract cosmological constraints, accurate theoretical predictions are needed. Currently such predictions can only be obtained from costly, precision numerical simulations. This paper is the third in a series aimed at constructing an accurate calibration of the nonlinear mass power spectrum on Mpc scales for a wide range of currently viable cosmological models, including dark energy. The first two papers addressed the numerical challenges, and the scheme by which an interpolator was built from a carefully chosen set of cosmological models. In this paper we introduce the "Coyote Univers"' simulation suite which comprises nearly 1,000 N-body simulations at different force and mass resolutions, spanning 38 wCDM cosmologies. This large simulation suite enables us to construct a prediction scheme, or emulator, for the nonlinear matter power spectrum accurate at the percent level out to k~1 h/Mpc. We describe the construction of the emulator, explain the tests performed to ensure its accuracy, and discuss how the central ideas may be extended to a wider range of cosmological models and applications. A power spectrum emulator code is released publicly as part of this paper.Comment: 10 pages, 10 figures, minor changes to address referee report, version v1.1 of the power spectrum emulator code can be downloaded at http://www.hep.anl.gov/cosmology/CosmicEmu/emu.html, includes now fortran wrapper and choice of any redshift between z=0 and z=1 (note: webpage now maintained at Argonne National Laboratory