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    The Integrated Bispectrum and Beyond

    Munshi, Dipak and Coles, Peter (2017) The Integrated Bispectrum and Beyond. Working Paper. arXiv.

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    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 {\em 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 {\em 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.

    Item Type: Monograph (Working Paper)
    Additional Information: Cite as: arXiv:1608.04345 [astro-ph.CO] (or arXiv:1608.04345v1 [astro-ph.CO] for this version). This is the preprint version of the article published at
    Keywords: Cosmology; Large Scale Structure; Methods; analytical; statistical; numerical;
    Academic Unit: Faculty of Science and Engineering > Theoretical Physics
    Item ID: 11376
    Identification Number:
    Depositing User: Peter Coles
    Date Deposited: 17 Oct 2019 16:48
    Publisher: arXiv
    Use Licence: This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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