Quantifying the Redshift Space Distortion of the Bispectrum I: Primordial Non-Gaussianity

Abstract

The anisotropy of the redshift space bispectrum contains a wealth of cosmological information. This anisotropy depends on the orientation of three vectors ${\mathbf{k}}_1,{\mathbf{k}}_2,{\mathbf{k}}_3$ with respect to the line of sight. Here we have decomposed the redshift space bispectrum in spherical harmonics which completely quantify this anisotropy. To illustrate this we consider linear redshift space distortion of the bispectrum arising from primordial non-Gaussianity. In the plane parallel approximation only the first four even $\ell$ multipoles have non-zero values, and we present explicit analytical expressions for all the non-zero multipoles {\it i.e.} upto $\ell =6,m=4$. The ratio of the different multipole moments to the real space bispectrum depends only on ${\beta }_1$ the linear redshift distortion parameter and the shape of the triangle. Considering triangles of all possible shapes, we have studied how this ratio depends on the shape of the triangle for ${\beta }_1=1$. We have also studied the ${\beta }_1$ dependence for some of the extreme triangle shapes. If measured in future, these multipole moments hold the potential of constraining ${\beta }_1$. The results presented here are also important if one wishes to constrain $f_{\text{NL}}$ using redshift surveys.

arXiv comment10 pages, 10 figures, accepted to MNRAS

References in corpus (44)

• Non-Gaussianity from Inflation: Theory and Observations
• 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
• Baryon Acoustic Oscillations in 2D: Modeling Redshift-space Power Spectrum from Perturbation Theory
• Reconstructing the history of structure formation using redshift distortions
• Measuring the cosmological constant with redshift surveys
• 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
• TASI Lectures on Inflation
• Nonlinear perturbation theory with halo bias and redshift-space distortions via the Lagrangian picture
• 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
• Fourier Analysis of Redshift Space Distortions and the Determination of Omega
• Planck 2018 results. IX. Constraints on primordial non-Gaussianity
• Constraints on Galaxy Bias, Matter Density, and Primordial Non--Gausianity from the PSCz Galaxy Redshift Survey
• Redshift Distortions as a Probe of Gravity
• The nonlinear redshift-space power spectrum of galaxies
• 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
• Bispectrum and Nonlinear Biasing of Galaxies: Perturbation Analysis, Numerical Simulation and SDSS Galaxy Clustering
• Large-scale bias in the Universe II: redshift space bispectrum
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: constraining modified gravity
• A Practical Computational Method for the Anisotropic Redshift-Space 3-Point Correlation Function
• Constraining primordial non-Gaussianity using two galaxy surveys and CMB lensing
• Searching for Modified Gravity: Scale and Redshift Dependent Constraints from Galaxy Peculiar Velocities
• Precision cosmology with redshift-space bispectrum: a perturbation theory based model at one-loop order
• The Stromlo-APM Redshift Survey III. Redshift Space Distortions, Omega and Bias
• Tensor Non-Gaussianity Search: Current Status and Future Prospects
• Estimating beta from redshift-space distortions in the 2dF galaxy survey
• CMB constraints on running non-Gaussianity
• Nonlinear redshift distortions: The two-point correlation function

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• The 21-cm bispectrum from neutral hydrogen islands at z < 6
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• Quantifying the redshift space distortion of the bispectrum III : Detection prospects of the multipole moments
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• Redshift-space galaxy bispectrum in presence of massive neutrinos: A multipole expansion approach for Euclid
• From ANN to BNN: Inferring Reionization Parameters using Uncertainty-aware Emulators of 21-cm Summaries
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• Tracing Signatures of Modified Gravity in Redshift-Space Galaxy Bispectrum Multipoles: Prospects for Euclid
• Probing the large-scale structure with 21cm-galaxy cross-bispectrum: Estimates from simulations and forecasts for upcoming cosmological surveys