Quantifying the redshift space distortion of the bispectrum III : Detection prospects of the multipole moments

Abstract

The redshift space anisotropy of the bispectrum is generally quantified using multipole moments. The possibility of measuring these multipoles in any survey depends on the level of statistical fluctuations. We present a formalism to compute the statistical fluctuations in the measurement of bispectrum multipoles for galaxy surveys. We consider specifications of a {\it Euclid} like galaxy survey and present two quantities: the signal-to-noise ratio (SNR) which quantifies the detectability of a multipole, and the rank correlation which quantifies the correlation in measurement errors between any two multipoles. Based on SNR values, we find that {\it Euclid} can potentially measure the bispectrum multipoles up to $\ell =4$ across various triangle shapes, formed by the three {\bf k} vectors in Fourier space. In general, SNR is maximum for the linear triangles. SNR values also depend on the scales and redshifts of observation. While, $\ell \le 2$ multipoles can be measured with $\mathrm{SNR}>5$ even at linear/quasi-linear ($k\lesssim 0.1{\mathrm{Mpc}}^{-1}$) scales, for $\ell >2$ multipoles, we require to go to small scales or need to increase bin sizes. For most multipole pairs, the errors are only weakly correlated across much of the triangle shapes barring a few in the vicinity of squeezed and stretched triangles. This makes it possible to combine the measurements of different multipoles to increase the effective SNR.

arXiv commentSubmitted to MNRAS main journal, 14 Pages, 8 Figures

References in corpus (74)

• Planck 2015 results. XIII. Cosmological parameters
• The Cosmic Linear Anisotropy Solving System (CLASS) II: Approximation schemes
• Large-Scale Structure of the Universe and Cosmological Perturbation Theory
• Non-Gaussianity from Inflation: Theory and Observations
• The imprints of primordial non-gaussianities on large-scale structure: scale dependent bias and abundance of virialized objects
• The 2dF Galaxy Redshift Survey: correlation functions, peculiar velocities and the matter density of the Universe
• A measurement of the cosmological mass density from clustering in the 2dF Galaxy Redshift Survey
• A test of the nature of cosmic acceleration using galaxy redshift distortions
• The 2dF Galaxy Redshift Survey: The bias of galaxies and the density of the Universe
• Redshift-Space Distortions, Pairwise Velocities and Nonlinearities
• Fingers of God
• Weighing Neutrinos with Galaxy Surveys
• Reconstructing the history of structure formation using redshift distortions
• 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
• Linear Redshift Distortions: A Review
• The Bispectrum as a Signature of Gravitational Instability in Redshift-Space
• The power spectrum and bispectrum of SDSS DR11 BOSS galaxies I: bias and gravity
• Probing Primordial Non-Gaussianity with Large-Scale Structure
• Primordial non-Gaussianity and Bispectrum Measurements in the Cosmic Microwave Background and Large-Scale Structure
• Large-scale bias in the Universe: bispectrum method
• The Bispectrum of IRAS Galaxies
• Constraints on Galaxy Bias, Matter Density, and Primordial Non--Gausianity from the PSCz Galaxy Redshift Survey
• Measuring neutrino masses with large-scale structure: Euclid forecast with controlled theoretical error
• Cosmological information in the redshift-space bispectrum
• Redshift Distortions as a Probe of Gravity
• Constraining $M_{\nu }$ with the Bispectrum II: The Total Information Content of the Galaxy Bispectrum
• Modelling the number density of Halpha emitters for future spectroscopic near-IR space missions
• Redshift space bias and beta from the halo model
• The redshift space power spectrum in the halo model
• The VIMOS Public Extragalactic Redshift Survey (VIPERS). Gravity test from the combination of redshift-space distortions and galaxy-galaxy lensing at $0.5<z<1.2$
• The CMB Bispectrum
• The Galaxy Power Spectrum and Bispectrum in Redshift Space
• A complete FFT-based decomposition formalism for the redshift-space bispectrum
• The Three-Point Correlation Function of Luminous Red Galaxies in the Sloan Digital Sky Survey
• Bispectrum and Nonlinear Biasing of Galaxies: Perturbation Analysis, Numerical Simulation and SDSS Galaxy Clustering
• Large-scale bias in the Universe II: redshift space bispectrum
• Covariance of cross-correlations: towards efficient measures for large-scale structure
• The 2dF Galaxy Redshift Survey: higher order galaxy correlation functions
• $Euclid$ preparation: XV. Forecasting cosmological constraints for the $Euclid$ and CMB joint analysis
• A Detection of the Baryon Acoustic Oscillation Features in the SDSS BOSS DR12 Galaxy Bispectrum
• The Three-point Correlation Function of Galaxies Determined from the 2dF Galaxy Redshift Survey
• Perturbation theory approach to predict the covariance matrices of the galaxy power spectrum and bispectrum in redshift space
• Where are the Luminous Red Galaxies (LRGs)? Using correlation measurements and lensing to relate LRGs to dark matter halos
• Galaxy redshift-space bispectrum: the Importance of Being Anisotropic
• The Large-Scale 3-point correlation function of SDSS Luminous Red Galaxies
• Information Content of the Angular Multipoles of Redshift-Space Galaxy Bispectrum
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: constraining modified gravity
• Modeling the large-scale redshift-space 3-point correlation function of galaxies
• A Practical Computational Method for the Anisotropic Redshift-Space 3-Point Correlation Function
• Constraining primordial non-Gaussianity using two galaxy surveys and CMB lensing
• Clustering of Luminous Red Galaxies III: Detection of the Baryon Acoustic Peak in the 3-point Correlation Function
• Searching for Modified Gravity: Scale and Redshift Dependent Constraints from Galaxy Peculiar Velocities
• Enhancing BOSS bispectrum cosmological constraints with maximal compression
• Precision cosmology with redshift-space bispectrum: a perturbation theory based model at one-loop order
• Information content in the redshift-space galaxy power spectrum and bispectrum
• Galaxy power spectrum in redshift space: combining perturbation theory with the halo model
• The clustering of galaxies and galaxy clusters: constraints on primordial non-Gaussianity from future wide-field surveys
• Tensor Non-Gaussianity Search: Current Status and Future Prospects
• Quantifying the Redshift Space Distortion of the Bispectrum I: Primordial Non-Gaussianity
• The Stromlo-APM Redshift Survey III. Redshift Space Distortions, Omega and Bias
• The dipole of the galaxy bispectrum
• Estimating beta from redshift-space distortions in the 2dF galaxy survey
• Neutrino mass and dark energy constraints from redshift-space distortions
• Impacts of satellite galaxies on the redshift-space distortions
• Modelling redshift-space distortion in the post-reionization $\mathrm{HI}$ 21-cm power spectrum
• Quantifying the Redshift Space Distortion of the Bispectrum II: Induced Non-Gaussianity at Second Order Perturbation
• CMB constraints on running non-Gaussianity
• Modelling the matter bispectrum at small scales in modified gravity
• Redshift space distortions of the {\rm HI} 21-cm intensity mapping signal due to the internal motions within galaxies
• Multipoles of the relativistic galaxy bispectrum
• Nonlinear redshift distortions: The two-point correlation function
• Fingers-of-God effect of infalling satellite galaxies
• Higher multipoles of the galaxy bispectrum in redshift space
• Constraints on Running of Non-Gaussianity from Large Scale Structure Probes

Cited by in corpus (8)

• Cosmology with the Galaxy Bispectrum Multipoles: Optimal Estimation and Application to BOSS Data
• Probing the Anisotropy and Non-Gaussianity in the Redshift Space through the Conditional Moments of the First Derivative
• Brisk estimator for the angular multipoles of the redshift space bispectrum
• The size and shape dependence of the SDSS galaxy bispectrum
• Mixing Bispectrum Multipoles Under Geometric Distortions
• Impact of Redshift Space Distortion on Persistent Homology of cosmic matter density field
• Redshift-space galaxy bispectrum in presence of massive neutrinos: A multipole expansion approach for Euclid
• Tracing Signatures of Modified Gravity in Redshift-Space Galaxy Bispectrum Multipoles: Prospects for Euclid