551 research outputs found
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
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