The Matter Bispectrum in N-body Simulations with non-Gaussian Initial Conditions

We present measurements of the dark matter bispectrum in N-body simulations with non-Gaussian initial conditions of the local kind for a large variety of triangular configurations and compare them with predictions from Eulerian Perturbation Theory up to one-loop corrections. We find that the effects of primordial non-Gaussianity at large scales, when compared to Perturbation Theory, are well described by the initial component of the matter bispectrum, linearly extrapolated at the redshift of interest. In addition, we find that, for f_NL=100, the nonlinear corrections due to non-Gaussian initial conditions are of the order of ~3, 4% for generic triangles up to ~20% for squeezed configurations, at any redshift. We show that the predictions of Perturbation Theory at tree-level fail to describe the simulation results at redshift z=0 already at scales corresponding to k ~ 0.02 - 0.08 h/Mpc, depending on the triangle, while one-loop corrections can significantly extend their validity to smaller scales. At higher redshift, one-loop Perturbation Theory provides indeed quite accurate predictions, particularly with respect to the relative correction due to primordial non-Gaussianity.Comment: 17 pages, 7 figures. Revised to match journal version with updated references. Accepted for publication in MNRAS

Tracing The Sound Horizon Scale With Photometric Redshift Surveys

We propose a new method for cosmological parameters extraction using the baryon acoustic oscillation scale as a standard ruler in deep galaxy surveys with photometric determination of redshifts. The method consists in a simple empirical parametric fit to the angular 2-point correlation function w(theta). It is parametrized as a power law to describe the continuum plus a Gaussian to describe the BAO bump. The location of the Gaussian is used as the basis for the measurement of the sound horizon scale. This method, although simple, actually provides a robust estimation, since the inclusion of the power law and the use of the Gaussian removes the shifts which affect the local maximum. We discuss the effects of projection bias, non-linearities, redshift space distortions and photo-z precision, and apply our method to a mock catalog of the Dark Energy Survey, built upon a large N-body simulation provided by the MICE collaboration. We discuss the main systematic errors associated to our method and show that they are dominated by the photo-z uncertainty.Comment: 12 pages, 12 figures, published online in MNRAS, 25 October 201

The matter bispectrum in N-body simulations with non-Gaussian initial conditions

We present measurements of the dark matter bispectrum in N-body simulations with non-Gaussian initial conditions of the local kind for a large variety of triangular configurations and compare them with predictions from Eulerian perturbation theory up to one-loop corrections. We find that the effects of primordial non-Gaussianity at large scales, when compared to perturbation theory, are well described by the initial component of the matter bispectrum, linearly extrapolated at the redshift of interest. In addition, we find that for fNL= 100, the non-linear corrections due to non-Gaussian initial conditions are of the order of ∼3-4 per cent for generic triangles and up to ∼20 per cent for squeezed configurations, at any redshift. We show that the predictions of perturbation theory at the tree level fail to describe the simulation results at redshift z= 0 at scales corresponding to k∼ 0.02-0.08 h Mpc−1, depending on the triangle, while one-loop corrections can significantly extend their validity to smaller scales. At higher redshift, one-loop perturbation theory indeed provides quite accurate predictions, particularly with respect to the relative correction due to primordial non-Gaussianit

Transients from Initial Conditions in Cosmological Simulations

We study the impact of setting initial conditions in numerical simulations using the standard procedure based on the Zel'dovich approximation (ZA). As it is well known from perturbation theory, ZA initial conditions have incorrect second and higher-order growth and therefore excite long-lived transients in the evolution of the statistical properties of density and velocity fields. We also study the improvement brought by using more accurate initial conditions based on second-order Lagrangian perturbation theory (2LPT). We show that 2LPT initial conditions reduce transients significantly and thus are much more appropriate for numerical simulations devoted to precision cosmology. Using controlled numerical experiments with ZA and 2LPT initial conditions we show that simulations started at redshift z_i=49 using the ZA underestimate the power spectrum in the nonlinear regime by about 2,4,8 % at z=0,1,3 respectively, whereas the mass function of dark matter halos is underestimated by 5% at m=10^15 M_sun/h (z=0) and 10% at m=2x10^14M_sun/h (z=1). The clustering of halos is also affected to the few percent level at z=0. These systematics effects are typically larger than statistical uncertainties in recent mass function and power spectrum fitting formulae extracted from numerical simulations. At large scales, the measured transients in higher-order correlations can be understood from first principle calculations based on perturbation theory.Comment: 14 pages, 14 figures, code to generate 2LPT initial conditions available at http://cosmo.nyu.edu/roman/2LPT . Typos corrected, Fig.13 symbols consistent with Fig.11,1

Power spectrum for the small-scale Universe

The first objects to arise in a cold dark matter universe present a daunting challenge for models of structure formation. In the ultra small-scale limit, CDM structures form nearly simultaneously across a wide range of scales. Hierarchical clustering no longer provides a guiding principle for theoretical analyses and the computation time required to carry out credible simulations becomes prohibitively high. To gain insight into this problem, we perform high-resolution (N=720^3 - 1584^3) simulations of an Einstein-de Sitter cosmology where the initial power spectrum is P(k) propto k^n, with -2.5 < n < -1. Self-similar scaling is established for n=-1 and n=-2 more convincingly than in previous, lower-resolution simulations and for the first time, self-similar scaling is established for an n=-2.25 simulation. However, finite box-size effects induce departures from self-similar scaling in our n=-2.5 simulation. We compare our results with the predictions for the power spectrum from (one-loop) perturbation theory and demonstrate that the renormalization group approach suggested by McDonald improves perturbation theory's ability to predict the power spectrum in the quasilinear regime. In the nonlinear regime, our power spectra differ significantly from the widely used fitting formulae of Peacock & Dodds and Smith et al. and a new fitting formula is presented. Implications of our results for the stable clustering hypothesis vs. halo model debate are discussed. Our power spectra are inconsistent with predictions of the stable clustering hypothesis in the high-k limit and lend credence to the halo model. Nevertheless, the fitting formula advocated in this paper is purely empirical and not derived from a specific formulation of the halo model.Comment: 30 pages including 10 figures; accepted for publication in MNRA

Cosmology and the Bispectrum

The present spatial distribution of galaxies in the Universe is non-Gaussian, with 40% skewness in 50 Mpc/h spheres, and remarkably little is known about the information encoded in it about cosmological parameters beyond the power spectrum. In this work we present an attempt to bridge this gap by studying the bispectrum, paying particular attention to a joint analysis with the power spectrum and their combination with CMB data. We address the covariance properties of the power spectrum and bispectrum including the effects of beat coupling that lead to interesting cross-correlations, and discuss how baryon acoustic oscillations break degeneracies. We show that the bispectrum has significant information on cosmological parameters well beyond its power in constraining galaxy bias, and when combined with the power spectrum is more complementary than combining power spectra of different samples of galaxies, since non-Gaussianity provides a somewhat different direction in parameter space. In the framework of flat cosmological models we show that most of the improvement of adding bispectrum information corresponds to parameters related to the amplitude and effective spectral index of perturbations, which can be improved by almost a factor of two. Moreover, we demonstrate that the expected statistical uncertainties in sigma8 of a few percent are robust to relaxing the dark energy beyond a cosmological constant