Matter trispectrum: theoretical modelling and comparison to N-body simulations

Abstract

The power spectrum has long been the workhorse summary statistics for large-scale structure cosmological analyses. However, gravitational non-linear evolution moves precious cosmological information from the two-point statistics (such as the power spectrum) to higher-order correlations. Moreover, information about the primordial non-Gaussian signal lies also in higher-order correlations. Without tapping into these, that information remains hidden. While the three-point function (or the bispectrum), even if not extensively, has been studied and applied to data, there has been only limited discussion about the four point/trispectrum. This is because the high-dimensionality of the statistics (in real space a skew-quadrilateral has 6 degrees of freedom), and the high number of skew-quadrilaterals, make the trispectrum numerically and algorithmically very challenging. Here we address this challenge by introducing the i-trispectrum, an integrated trispectrum that only depends on four $k$-modes moduli. We model and measure the matter i-trispectrum from a set of 5000 \textsc{Quijote} N-body simulations both in real and redshift space, finding good agreement between simulations outputs and model up to mildly non-linear scales. Using the power spectrum, bispectrum and i-trispectrum joint data-vector covariance matrix estimated from the simulations, we begin to quantify the added-value provided by the i-trispectrum. In particular, we forecast the i-trispectrum improvements on constraints on the local primordial non-Gaussianity amplitude parameters $f_{\mathrm{nl}}$ and $g_{\mathrm{nl}}$. For example, using the full joint data-vector, we forecast $f_{\mathrm{nl}}$ constraints up to two times ($\sim 32\%$) smaller in real (redshift) space than those obtained without i-trispectrum.

arXiv commentaccepted: 6th of November 2020, published: 11th of January 2021 , 64 pages (35 pages for the main text), 15 figures

References in corpus (86)

• Non-Gaussian features of primordial fluctuations in single field inflationary models
• Cosmological SPH simulations: A hybrid multi-phase model for star formation
• Stable clustering, the halo model and nonlinear cosmological power spectra
• Non-Gaussianity from Inflation: Theory and Observations
• Revising the Halofit Model for the Nonlinear Matter Power Spectrum
• Acoustic Signatures in the Primary Microwave Background Bispectrum
• Karhunen-Loeve eigenvalue problems in cosmology: how should we tackle large data sets?
• Why your model parameter confidences might be too optimistic -- unbiased estimation of the inverse covariance matrix
• The imprints of primordial non-gaussianities on large-scale structure: scale dependent bias and abundance of virialized objects
• Extragalactic Science, Cosmology and Galactic Archaeology with the Subaru Prime Focus Spectrograph (PFS)
• Transients from Initial Conditions in Cosmological Simulations
• Single field consistency relation for the 3-point function
• The 2dF Galaxy Redshift Survey: The bias of galaxies and the density of the Universe
• The Cosmic Linear Anisotropy Solving System (CLASS) I: Overview
• Fingers of God
• The effect of primordial non-Gaussianity on halo bias
• The DESI Experiment, a whitepaper for Snowmass 2013
• The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: RSD measurement from the power spectrum and bispectrum of the DR12 BOSS galaxies
• Large-scale structure, the cosmic microwave background, and primordial non-gaussianity
• The Quijote simulations
• Massive Neutrinos and the Non-linear Matter Power Spectrum
• Cosmology with Phase 1 of the Square Kilometre Array; Red Book 2018: Technical specifications and performance forecasts
• Cosmology and the Bispectrum
• Accurate halo-model matter power spectra with dark energy, massive neutrinos and modified gravitational forces
• Parameter inference with estimated covariance matrices
• Accurate Estimators of Correlation Functions in Fourier Space
• The power spectrum and bispectrum of SDSS DR11 BOSS galaxies I: bias and gravity
• Fast likelihood-free cosmology with neural density estimators and active learning
• Fast Estimators for Redshift-Space Clustering
• Probing Primordial Non-Gaussianity with Large-Scale Structure
• The Bispectrum: From Theory to Observations
• Large-scale Bias and Efficient Generation of Initial Conditions for Non-Local Primordial Non-Gaussianity
• The Bispectrum of IRAS Galaxies
• Planck 2018 results. IX. Constraints on primordial non-Gaussianity
• Structure formation from non-Gaussian initial conditions: multivariate biasing, statistics, and comparison with N-body simulations
• Primordial non-Gaussianity, scale-dependent bias, and the bispectrum of galaxies
• Constraining Primordial non-Gaussianity with Bispectrum and Power Spectum from Upcoming Optical and Radio Surveys
• Constraining $M_{\nu }$ with the Bispectrum I: Breaking Parameter Degeneracies
• Cosmological information in the redshift-space bispectrum
• Redshift-weighted constraints on primordial non-Gaussianity from the clustering of the eBOSS DR14 quasars in Fourier space
• Primordial non-Gaussianity in the Bispectrum of the Halo Density Field
• Galaxy Power Spectrum Multipoles Covariance in Perturbation Theory
• Assessment of the Information Content of the Power Spectrum and Bispectrum
• On the assumption of Gaussianity for cosmological two-point statistics and parameter dependent covariance matrices
• An improved fitting formula for the dark matter bispectrum
• Cubic Halo Bias in Eulerian and Lagrangian Space
• 1-loop Perturbative Corrections to the Matter and Galaxy Bispectrum with non-Gaussian Initial Conditions
• A complete FFT-based decomposition formalism for the redshift-space bispectrum
• Galaxy bispectrum, primordial non-Gaussianity and redshift space distortions
• Galaxy Bias and Halo-Occupation Numbers from Large-Scale Clustering
• Beyond LIMD bias: a measurement of the complete set of third-order halo bias parameters
• The Trispectrum in the Effective Field Theory of Large Scale Structure
• Perturbation theory approach to predict the covariance matrices of the galaxy power spectrum and bispectrum in redshift space
• Galaxy redshift-space bispectrum: the Importance of Being Anisotropic
• Perturbative approach to covariance matrix of the matter power spectrum
• The trispectrum of 21-cm background anisotropies as a probe of primordial non-Gaussianity
• On the trispectrum as a gaussian test for cosmology
• Cosmological inference from Bayesian forward modelling of deep galaxy redshift surveys
• The Halo Bispectrum in N-body Simulations with non-Gaussian Initial Conditions
• Maximal compression of the redshift space galaxy power spectrum and bispectrum
• The Pursuit of Non-Gaussian Fluctuations in the Cosmic Microwave Background
• Dark matter and halo bispectrum in redshift space: theory and applications
• The Trispectrum of the 4 Year COBE-DMR data
• Enhancing BOSS bispectrum cosmological constraints with maximal compression
• New Optimised Estimators for the Primordial Trispectrum
• Optimal Trispectrum Estimators and WMAP Constraints
• The trispectrum of the Cosmic Microwave Background on sub-degree angular scales: an analysis of the BOOMERanG data
• Cosmic Shear: Inference from Forward Models
• Bispectrum covariance in the flat-sky limit
• The CMB Bispectrum, Trispectrum, non-Gaussianity, and the Cramer-Rao Bound
• Non-local bias in the halo bispectrum with primordial non-Gaussianity
• Lagrangian bias of generic large-scale structure tracers
• Graph Database Solution for Higher Order Spatial Statistics in the Era of Big Data
• A fitting formula for the non-Gaussian contribution to the lensing power spectrum covariance
• Covariance of the matter power spectrum including the survey window function effect: N-body simulations vs. fifth-order perturbation theory on grid
• Optimal analysis of the CMB trispectrum
• Constraints on Patchy Reionization from Planck CMB Temperature Trispectrum
• Trispectrum estimation in various models of equilateral type non-Gaussianity
• Cosmological parameter inference from galaxy clustering: The effect of the posterior distribution of the power spectrum
• Trispectrum estimator in equilateral type non-Gaussian models
• Cosmological Angular Trispectra and Non-Gaussian Covariance
• Planck Trispectrum Constraints on Primordial Non-Gaussianity at Cubic Order
• Efficient parallel algorithm for estimating higher-order polyspectra
• Constraining the WMAP9 bispectrum and trispectrum with needlets
• Measuring the Energy Scale of Inflation with Large Scale Structures
• GEOMAX: beyond linear compression for 3pt galaxy clustering statistics

Cited by in corpus (35)

• The CAMELS project: Cosmology and Astrophysics with MachinE Learning Simulations
• Detecting Neutrino Mass by Combining Matter Clustering, Halos, and Voids
• The GIGANTES dataset: precision cosmology from voids in the machine learning era
• Joint analysis of anisotropic power spectrum, bispectrum and trispectrum: application to N-body simulations
• Cosmological direct detection of dark energy: non-linear structure formation signatures of dark energy scattering with visible matter
• Learning cosmology and clustering with cosmic graphs
• Cosmology with one galaxy?
• The Covariance of Squeezed Bispectrum Configurations
• Information Content of Higher-Order Galaxy Correlation Functions
• Precise Calibration of the One-Loop Bispectrum in the Effective Field Theory of Large Scale Structure
• The two-loop bispectrum of large-scale structure
• NECOLA: Towards a Universal Field-level Cosmological Emulator
• EFTofLSS meets simulation-based inference: ${\sigma }_8$ from biased tracers
• A First Detection of the Connected 4-Point Correlation Function of Galaxies Using the BOSS CMASS Sample
• Quijote-PNG: Quasi-maximum likelihood estimation of Primordial Non-Gaussianity in the non-linear dark matter density field
• Precise Calibration of the One-Loop Trispectrum in the Effective Field Theory of Large Scale Structure
• Joint velocity and density reconstruction of the Universe with nonlinear differentiable forward modeling
• Modeling the Marked Spectrum of Matter and Biased Tracers in Real- and Redshift-Space
• Integrated trispectrum detection from BOSS DR12 NGC CMASS
• Super-sample covariance of the power spectrum, bispectrum, halos, voids, and their cross covariances
• Quantification of high dimensional non-Gaussianities and its implication to Fisher analysis in cosmology
• Weak Lensing Trispectrum and Kurt-Spectra
• GEO-FPT: a model of the galaxy bispectrum at mildly non-linear scales
• Inpainting hydrodynamical maps with deep learning
• A Model for the Redshift-Space Galaxy 4-Point Correlation Function
• Cosmology from Point Clouds with Dark Matter Halos from the Quijote Simulations
• Breaking parity: the case of the trispectrum from chiral scalar-tensor theories of gravity
• Mixing Bispectrum Multipoles Under Geometric Distortions
• The Odd-Parity Part of the Observed Galaxy Trispectrum
• A New Estimator for Phase Statistics
• Multi-wavelength spectroscopic probes: prospects for primordial non-Gaussianity and relativistic effects
• New tests of dark sector interactions from the full-shape galaxy power spectrum
• About One-point Statistics of the Ratio of Two Fourier-transformed Cosmic Fields and an Application
• On Weak Lensing Response Functions
• nuGAN: Generative Adversarial Emulator for Cosmic Web with Neutrinos