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Title: The integrated bispectrum and beyond

Abstract

The position-dependent power spectrum has been recently proposed as a descriptor of gravitationally induced non-Gaussianity in galaxy clustering, as it is sensitive to the 'soft limit' of the bispectrum (i.e. when one of the wave number tends to zero). We generalise this concept to higher order and clarify their relationship to other known statistics such as the skew-spectrum, the kurt-spectra and their real-space counterparts the cumulants correlators. Using the Hierarchical Ansatz (HA) as a toy model for the higher order correlation hierarchy, we show how in the soft limit, polyspectra at a given order can be identified with lower order polyspectra with the same geometrical dependence but with renormalised amplitudes expressed in terms of amplitudes of the original polyspectra. We extend the concept of position-dependent bispectrum to bispectrum of the divergence of the velocity field Θ and mixed multispectra involving δ and Θ in the 3D perturbative regime. To quantify the effects of transients in numerical simulations, we also present results for lowest order in Lagrangian perturbation theory (LPT) or the Zel'dovich approximation (ZA). Finally, we discuss how to extend the position-dependent spectrum concept to encompass cross-spectra. And finally study the application of this concept to two dimensions (2D), formore » projected galaxy maps, convergence κ maps from weak-lensing surveys or maps of CMB secondaries e.g. the frequency cleaned y -parameter maps of thermal Sunyaev-Zel'dovich (tSZ) effect from CMB surveys.« less

Authors:
 [1];  [2]
  1. Astronomy Centre, School of Mathematical and Physical Sciences, University of Sussex, Brighton BN1 9QH (United Kingdom)
  2. School of Physics and Astronomy, Cardiff University, Queen's Buildings, The Parade, Cardiff CF24 3AA (United Kingdom)
Publication Date:
OSTI Identifier:
22680044
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 02; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; AMPLITUDES; APPROXIMATIONS; COMPUTERIZED SIMULATION; CONVERGENCE; CORRELATIONS; DISTURBANCES; GALAXIES; GRAVITATIONAL LENSES; LAGRANGIAN FUNCTION; PERTURBATION THEORY; RELICT RADIATION; SPACE; SPECTRA; VELOCITY

Citation Formats

Munshi, Dipak, and Coles, Peter, E-mail: D.Munshi@sussex.ac.uk, E-mail: P.Coles@sussex.ac.uk. The integrated bispectrum and beyond. United States: N. p., 2017. Web. doi:10.1088/1475-7516/2017/02/010.
Munshi, Dipak, & Coles, Peter, E-mail: D.Munshi@sussex.ac.uk, E-mail: P.Coles@sussex.ac.uk. The integrated bispectrum and beyond. United States. doi:10.1088/1475-7516/2017/02/010.
Munshi, Dipak, and Coles, Peter, E-mail: D.Munshi@sussex.ac.uk, E-mail: P.Coles@sussex.ac.uk. Wed . "The integrated bispectrum and beyond". United States. doi:10.1088/1475-7516/2017/02/010.
@article{osti_22680044,
title = {The integrated bispectrum and beyond},
author = {Munshi, Dipak and Coles, Peter, E-mail: D.Munshi@sussex.ac.uk, E-mail: P.Coles@sussex.ac.uk},
abstractNote = {The position-dependent power spectrum has been recently proposed as a descriptor of gravitationally induced non-Gaussianity in galaxy clustering, as it is sensitive to the 'soft limit' of the bispectrum (i.e. when one of the wave number tends to zero). We generalise this concept to higher order and clarify their relationship to other known statistics such as the skew-spectrum, the kurt-spectra and their real-space counterparts the cumulants correlators. Using the Hierarchical Ansatz (HA) as a toy model for the higher order correlation hierarchy, we show how in the soft limit, polyspectra at a given order can be identified with lower order polyspectra with the same geometrical dependence but with renormalised amplitudes expressed in terms of amplitudes of the original polyspectra. We extend the concept of position-dependent bispectrum to bispectrum of the divergence of the velocity field Θ and mixed multispectra involving δ and Θ in the 3D perturbative regime. To quantify the effects of transients in numerical simulations, we also present results for lowest order in Lagrangian perturbation theory (LPT) or the Zel'dovich approximation (ZA). Finally, we discuss how to extend the position-dependent spectrum concept to encompass cross-spectra. And finally study the application of this concept to two dimensions (2D), for projected galaxy maps, convergence κ maps from weak-lensing surveys or maps of CMB secondaries e.g. the frequency cleaned y -parameter maps of thermal Sunyaev-Zel'dovich (tSZ) effect from CMB surveys.},
doi = {10.1088/1475-7516/2017/02/010},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 02,
volume = 2017,
place = {United States},
year = {Wed Feb 01 00:00:00 EST 2017},
month = {Wed Feb 01 00:00:00 EST 2017}
}