scholarly journals Suppressing cosmic variance with paired-and-fixed cosmological simulations: average properties and covariances of dark matter clustering statistics

2020 ◽  
Vol 496 (3) ◽  
pp. 3862-3869 ◽  
Author(s):  
Anatoly Klypin ◽  
Francisco Prada ◽  
Joyce Byun
Keyword(s):  
Dark Matter ◽  
Power Spectrum ◽  
Initial Conditions ◽  
Cosmological Parameters ◽  
Average Density ◽  
Covariance Matrices ◽  
Acoustic Oscillations ◽  
Galaxy Clustering ◽  
The Mean ◽  
Statistical Noise

ABSTRACT Making cosmological inferences from the observed galaxy clustering requires accurate predictions for the mean clustering statistics and their covariances. Those are affected by cosmic variance – the statistical noise due to the finite number of harmonics. The cosmic variance can be suppressed by fixing the amplitudes of the harmonics instead of drawing them from a Gaussian distribution predicted by the inflation models. Initial realizations also can be generated in pairs with 180○ flipped phases to further reduce the variance. Here, we compare the consequences of using paired-and-fixed versus Gaussian initial conditions on the average dark matter clustering and covariance matrices predicted from N-body simulations. As in previous studies, we find no measurable differences between paired-and-fixed and Gaussian simulations for the average density distribution function, power spectrum, and bispectrum. Yet, the covariances from paired-and-fixed simulations are suppressed in a complicated scale- and redshift-dependent way. The situation is particularly problematic on the scales of Baryon acoustic oscillations where the covariance matrix of the power spectrum is lower by only $\sim 20{{\ \rm per\ cent}}$ compared to the Gaussian realizations, implying that there is not much of a reduction of the cosmic variance. The non-trivial suppression, combined with the fact that paired-and-fixed covariances are noisier than from Gaussian simulations, suggests that there is no path towards obtaining accurate covariance matrices from paired-and-fixed simulations – result, that is theoretically expected and accepted in the field. Because the covariances are crucial for the observational estimates of galaxy clustering statistics and cosmological parameters, paired-and-fixed simulations, though useful for some applications, cannot be used for the production of mock galaxy catalogues.

scholarly journals The anisotropy of the power spectrum in periodic cosmological simulations

2021 ◽  
Vol 503 (4) ◽  
pp. 5638-5645
Author(s):  
Gábor Rácz ◽  
István Szapudi ◽  
István Csabai ◽  
László Dobos
Keyword(s):  
Dark Matter ◽  
Power Spectrum ◽  
Large Scale ◽  
Cold Dark Matter ◽  
Initial Conditions ◽  
Power Spectra ◽  
Cosmological Simulations ◽  
Spherical Collapse ◽  
Lower Amplitude ◽  
Hydrodynamical Simulations

ABSTRACT The classical gravitational force on a torus is anisotropic and always lower than Newton’s 1/r2 law. We demonstrate the effects of periodicity in dark matter only N-body simulations of spherical collapse and standard Lambda cold dark matter (ΛCDM) initial conditions. Periodic boundary conditions cause an overall negative and anisotropic bias in cosmological simulations of cosmic structure formation. The lower amplitude of power spectra of small periodic simulations is a consequence of the missing large-scale modes and the equally important smaller periodic forces. The effect is most significant when the largest mildly non-linear scales are comparable to the linear size of the simulation box, as often is the case for high-resolution hydrodynamical simulations. Spherical collapse morphs into a shape similar to an octahedron. The anisotropic growth distorts the large-scale ΛCDM dark matter structures. We introduce the direction-dependent power spectrum invariant under the octahedral group of the simulation volume and show that the results break spherical symmetry.

scholarly journals Turnaround radius of galaxy clusters in N-body simulations

2020 ◽  
Vol 639 ◽  
pp. A122 ◽  
Author(s):  
Giorgos Korkidis ◽  
Vasiliki Pavlidou ◽  
Konstantinos Tassis ◽  
Evangelia Ntormousi ◽  
Theodore N. Tomaras ◽  
...  
Keyword(s):  
Dark Matter ◽  
Galaxy Clusters ◽  
Cosmological Parameters ◽  
Three Dimensional ◽  
Average Density ◽  
Matter Density ◽  
Tidal Forces ◽  
Spherical Collapse ◽  
Collapse Model ◽  
Model C

Aims. We use N-body simulations to examine whether a characteristic turnaround radius, as predicted from the spherical collapse model in a ΛCDM Universe, can be meaningfully identified for galaxy clusters in the presence of full three-dimensional effects. Methods. We use The Dark Sky Simulations and Illustris-TNG dark-matter-only cosmological runs to calculate radial velocity profiles around collapsed structures, extending out to many times the virial radius R200. There, the turnaround radius can be unambiguously identified as the largest nonexpanding scale around a center of gravity. Results. We find that: (a) a single turnaround scale can meaningfully describe strongly nonspherical structures. (b) For halos of masses M200 >  1013 M⊙, the turnaround radius Rta scales with the enclosed mass Mta as Mta1/3, as predicted by the spherical collapse model. (c) The deviation of Rta in simulated halos from the spherical collapse model prediction is relatively insensitive to halo asphericity. Rather, it is sensitive to the tidal forces due to massive neighbors when these are present. (d) Halos exhibit a characteristic average density within the turnaround scale. This characteristic density is dependent on cosmology and redshift. For the present cosmic epoch and for concordance cosmological parameters (Ωm ∼ 0.3; ΩΛ ∼ 0.7) turnaround structures exhibit a density contrast with the matter density of the background Universe of δ ∼ 11. Thus, Rta is equivalent to R11 – in a way that is analogous to defining the “virial” radius as R200 – with the advantage that R11 is shown in this work to correspond to a kinematically relevant scale in N-body simulations.

scholarly journals The information content of Cosmic Infrared Background anisotropies

2019 ◽  
Author(s):  
Robert Reischke ◽  
Vincent Desjacques ◽  
Saleem Zaroubi
Keyword(s):  
Power Spectrum ◽  
Cosmological Parameters ◽  
Model Parameters ◽  
Mass Relation ◽  
Infrared Background ◽  
Cross Correlations ◽  
The Mean ◽  
Cosmic Infrared Background ◽  
Almost All ◽  
Halo Occupation Distribution

Abstract We use analytic computations to predict the power spectrum as well as the bispectrum of Cosmic Infrared Background (CIB) anisotropies. Our approach is based on the halo model and takes into account the mean luminosity-mass relation. The model is used to forecast the possibility to simultaneously constrain cosmological, CIB and halo occupation distribution (HOD) parameters in the presence of foregrounds. For the analysis we use wavelengths in eight frequency channels between 200 and 900 GHz with survey specifications given by Planck and LiteBird. We explore the sensitivity to the model parameters up to multipoles of ℓ = 1000 using auto- and cross-correlations between the different frequency bands. With this setting, cosmological, HOD and CIB parameters can be constrained to a few percent. Galactic dust is modeled by a power law and the shot noise contribution as a frequency dependent amplitude which are marginalized over. We find that dust residuals in the CIB maps only marginally influence constraints on standard cosmological parameters. Furthermore, the bispectrum yields tighter constraints (by a factor four in 1σ errors) on almost all model parameters while the degeneracy directions are very similar to the ones of the power spectrum. The increase in sensitivity is most pronounced for the sum of the neutrino masses. Due to the similarity of degeneracies a combination of both analysis is not needed for most parameters. This, however, might be due to the simplified bias description generally adopted in such halo model approaches.

scholarly journals Primordial power spectrum and cosmology from black-box galaxy surveys

2019 ◽  
Vol 490 (3) ◽  
pp. 4237-4253 ◽  
Author(s):  
Florent Leclercq ◽  
Wolfgang Enzi ◽  
Jens Jasche ◽  
Alan Heavens
Keyword(s):  
Power Spectrum ◽  
Numerical Models ◽  
A Priori ◽  
Cosmological Parameters ◽  
Physical Structure ◽  
Black Box ◽  
Acoustic Oscillations ◽  
Galaxy Surveys ◽  
Matter Power Spectrum ◽  
Primordial Power Spectrum

ABSTRACT We propose a new, likelihood-free approach to inferring the primordial matter power spectrum and cosmological parameters from arbitrarily complex forward models of galaxy surveys where all relevant statistics can be determined from numerical simulations, i.e. black boxes. Our approach, which we call simulator expansion for likelihood-free inference (selfi), builds upon approximate Bayesian computation using a novel effective likelihood, and upon the linearization of black-box models around an expansion point. Consequently, we obtain simple ‘filter equations’ for an effective posterior of the primordial power spectrum, and a straightforward scheme for cosmological parameter inference. We demonstrate that the workload is computationally tractable, fixed a priori, and perfectly parallel. As a proof of concept, we apply our framework to a realistic synthetic galaxy survey, with a data model accounting for physical structure formation and incomplete and noisy galaxy observations. In doing so, we show that the use of non-linear numerical models allows the galaxy power spectrum to be safely fitted up to at least kmax = 0.5 h Mpc−1, outperforming state-of-the-art backward-modelling techniques by a factor of ∼5 in the number of modes used. The result is an unbiased inference of the primordial matter power spectrum across the entire range of scales considered, including a high-fidelity reconstruction of baryon acoustic oscillations. It translates into an unbiased and robust inference of cosmological parameters. Our results pave the path towards easy applications of likelihood-free simulation-based inference in cosmology. We have made our code pyselfi and our data products publicly available at http://pyselfi.florent-leclercq.eu.

scholarly journals A Model for the Sequence of Elliptical Galaxies

1987 ◽  
Vol 117 ◽  
pp. 367-367
Author(s):  
Rosemary F. G. Wyse ◽  
Bernard J. T. Jones
Keyword(s):  
Dark Matter ◽  
Power Spectrum ◽  
Galaxy Formation ◽  
Cold Dark Matter ◽  
Initial Conditions ◽  
Elliptical Galaxy ◽  
Elliptical Galaxies ◽  
Density Fluctuations ◽  
Analytic Approximation ◽  
Non Linear

We present a simple model for the formation of elliptical galaxies, based on a binary clustering hierarchy of dark matter, the chemical enrichment of the gas at each level being controlled by supernovae. The initial conditions for the non-linear phases of galaxy formation are set by the post-recombination power spectrum of density fluctuations. We investigate two models for this power spectrum - the first is a straightforward power law, |δk|2 ∝ kn, and the second is Peeble's analytic approximation to the emergent spectrum in a universe dominated by cold dark matter. The normalisation is chosen such that on some scale, say M ∼ 1012M⊙, the objects that condense out have properties - radius and velocity dispersion - resembling ‘typical’ galaxies. There is some ambiguity in this due to the poorly determined mass-to-light ratio of a typical elliptical galaxy — we look at two normalisations, σ1D ∼ 350kms−1 and σ1D ∼ 140kms−1. The choice determines which of Compton cooling or hydrogen cooling is more important during the galaxy formation period. The non-linear behaviour of the perturbations is treated by the homogeneous sphere approximation.

scholarly journals Comparing approximate methods for mock catalogues and covariance matrices II: power spectrum multipoles

2019 ◽  
Vol 485 (2) ◽  
pp. 2806-2824 ◽  
Author(s):  
Linda Blot ◽  
Martin Crocce ◽  
Emiliano Sefusatti ◽  
Martha Lippich ◽  
Ariel G Sánchez ◽  
...  
Keyword(s):  
Growth Rate ◽  
Distribution Function ◽  
Power Spectrum ◽  
Probability Distribution Function ◽  
Initial Conditions ◽  
Covariance Matrices ◽  
Full Density ◽  
Model Parameters ◽  
Approximate Methods ◽  
Parameter Constraints

ABSTRACT We study the accuracy of several approximate methods for gravitational dynamics in terms of halo power spectrum multipoles and their estimated covariance matrix. We propagate the differences in covariances into parameter constraints related to growth rate of structure, Alcock–Paczynski distortions, and biasing. We consider seven methods in three broad categories: algorithms that solve for halo density evolution deterministically using Lagrangian trajectories (ICE–COLA, pinocchio, and peakpatch), methods that rely on halo assignment schemes on to dark matter overdensities calibrated with a target N-body run (halogen, patchy), and two standard assumptions about the full density probability distribution function (Gaussian and lognormal). We benchmark their performance against a set of three hundred N-body simulations, running similar sets of approximate simulations with matched initial conditions, for each method. We find that most methods reproduce the monopole to within $5{{\ \rm per\ cent}}$, while residuals for the quadrupole are sometimes larger and scale dependent. The variance of the multipoles is typically reproduced within $10{{\ \rm per\ cent}}$. Overall, we find that covariances built from approximate simulations yield errors on model parameters within $10{{\ \rm per\ cent}}$ of those from the N-body-based covariance.

scholarly journals The halo mass function in alternative dark matter models

2020 ◽  
Vol 493 (1) ◽  
pp. L11-L15 ◽  
Author(s):  
M R Lovell
Keyword(s):  
Dark Matter ◽  
Power Spectrum ◽  
Particle Physics ◽  
Mass Function ◽  
Small Scale ◽  
Acoustic Oscillations ◽  
Sterile Neutrinos ◽  
Matter Power Spectrum ◽  
Alternative Approach ◽  
Good Agreement

ABSTRACT The claimed detection of large amounts of substructure in lensing flux anomalies, and in Milky Way stellar stream gap statistics, has led to a step change in constraints on simple warm dark matter models. In this study, we compute predictions for the halo mass function both for these simple models and for comprehensive particle physics models of sterile neutrinos and dark acoustic oscillations. We show that the mass function fit of Lovell et al. underestimates the number of haloes less massive than the half-mode mass, $M_\mathrm {hm}$, by a factor of 2, relative to the extended Press–Schechter (EPS) method. The alternative approach of applying EPS to the Viel et al. matter power spectrum fit instead suggests good agreement at $M_\mathrm {hm}$ relative to the comprehensive model matter power spectrum results, although the number of haloes with mass $\rm{\lt} M_\mathrm {hm}$ is still suppressed due to the absence of small-scale power in the fitting function. Overall, we find that the number of dark matter haloes with masses $\rm{\lt} 10^{8}{\, \rm M_\odot }$ predicted by competitive particle physics models is underestimated by a factor of ∼2 when applying popular fitting functions, although careful studies that follow the stripping and destruction of subhaloes will be required in order to draw robust conclusions.

scholarly journals Deep learning dark matter map reconstructions from DES SV weak lensing data

2020 ◽  
Vol 492 (4) ◽  
pp. 5023-5029 ◽  
Author(s):  
Niall Jeffrey ◽  
François Lanusse ◽  
Ofer Lahav ◽  
Jean-Luc Starck
Keyword(s):  
Dark Matter ◽  
Deep Learning ◽  
Power Spectrum ◽  
Cosmological Parameters ◽  
Simulated Data ◽  
Wiener Filtering ◽  
Weak Lensing ◽  
Gaussian Shape ◽  
Non Linear ◽  
Mass Mapping

ABSTRACT We present the first reconstruction of dark matter maps from weak lensing observational data using deep learning. We train a convolution neural network with a U-Net-based architecture on over 3.6 × 105 simulated data realizations with non-Gaussian shape noise and with cosmological parameters varying over a broad prior distribution. We interpret our newly created dark energy survey science verification (DES SV) map as an approximation of the posterior mean P(κ|γ) of the convergence given observed shear. Our DeepMass1 method is substantially more accurate than existing mass-mapping methods. With a validation set of 8000 simulated DES SV data realizations, compared to Wiener filtering with a fixed power spectrum, the DeepMass method improved the mean square error (MSE) by 11 per cent. With N-body simulated MICE mock data, we show that Wiener filtering, with the optimal known power spectrum, still gives a worse MSE than our generalized method with no input cosmological parameters; we show that the improvement is driven by the non-linear structures in the convergence. With higher galaxy density in future weak lensing data unveiling more non-linear scales, it is likely that deep learning will be a leading approach for mass mapping with Euclid and LSST.

scholarly journals On the Reliability of Initial Conditions for Dissipationless Cosmological Simulations

2003 ◽  
Vol 20 (2) ◽  
pp. 173-183 ◽  
Author(s):  
Alexander Knebe ◽  
Alvaro Domínguez
Keyword(s):  
Power Spectrum ◽  
Fundamental Mode ◽  
Initial Conditions ◽  
Interparticle Distance ◽  
Particle Distributions ◽  
The Mean ◽  
Internal Properties ◽  
Correlation Properties ◽  
Random Nature ◽  
Simulation Volume

AbstractWe present the study of ten random realisations of a density field characterised by a cosmological power spectrum P(k) at redshift z = 50. The reliability of such initial conditions for N-body simulations is tested with respect to their correlation properties. The power spectrum P(k) and the mass variance σM(r) do not show detectable deviations from the desired behaviour in the intermediate range of scales between the mean interparticle distance and the simulation volume. The estimator for ξ(r) is too noisy to detect any reliable signal at the initial redshift z = 50. The particle distributions are then evolved forward until z = 0. This allows us to explore the cosmic variance stemming from the random nature of the initial conditions. With cosmic variance we mean the fact that a simulation represents a single realisation of the stochastic initial conditions whereas the real Universe contains many realisations of regions of the size of the box; this problem affects most importantly the scales at about the fundamental mode. We study morphological descriptors of the matter distribution such as the genus, as well as the internal properties of the largest object(s) forming in the box. We find that the scatter is at least comparable to the scatter in the fundamental mode.

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