{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/quantifying-the-redshift-space-distortion-of-1","title":"Quantifying the Redshift Space Distortion of the Bispectrum II: Induced Non-Gaussianity at Second Order Perturbation","arxiv_id":"2005.07066","date":"2020-05-14","proceeding":null,"authors":["Arindam Mazumdar","Somnath Bharadwaj","Debanjan Sarkar"],"abstract":"The anisotrpy of the redshift space bispectrum $B^s(\\mathbf{k_1},\\mathbf{k_2},\\mathbf{k_3})$, which contains a wealth of cosmological information, is completely quantified using multipole moments $\\bar{B}^m_{\\ell}(k_1,\\mu,t)$ where $k_1$, the length of the largest side, and $(\\mu,t)$ respectively quantify the size and shape of the triangle $(\\mathbf{k_1},\\mathbf{k_2},\\mathbf{k_3})$. We present analytical expressions for all the multipoles which are predicted to be non-zero ($\\ell \\le 8, m \\le 6$ ) at second order perturbation theory. The multipoles also depend on $\\beta_1,b_1$ and $\\gamma_2$, which quantify the linear redshift distortion parameter, linear bias and quadratic bias respectively. Considering triangles of all possible shapes, we analyse the shape dependence of all of the multipoles holding $k_1=0.2 \\, {\\rm Mpc}^{-1}, \\beta_1=1, b_1=1$ and $\\gamma_2=0$ fixed. The monopole $\\bar{B}^0_0$, which is positive everywhere, is minimum for equilateral triangles. $\\bar{B}_0^0$ increases towards linear triangles, and is maximum for linear triangles close to the squeezed limit. Both $\\bar{B}^0_{2}$ and $\\bar{B}^0_4$ are similar to $\\bar{B}^0_0$, however the quadrupole $\\bar{B}^0_2$ exceeds $\\bar{B}^0_0$ over a significant range of shapes. The other multipoles, many of which become negative, have magnitudes smaller than $\\bar{B}^0_0$. In most cases the maxima or minima, or both, occur very close to the squeezed limit. $\\mid \\bar{B}^m_{\\ell} \\mid $ is found to decrease rapidly if $\\ell$ or $m$ are increased. The shape dependence shown here is characteristic of non-linear gravitational clustering. Non-linear bias, if present, will lead to a different shape dependence.","url_abs":"http://arxiv.org/abs/2005.07066v2","url_pdf":"http://arxiv.org/pdf/2005.07066v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"quantifying-the-redshift-space-distortion-of-1","repo_url":"https://github.com/arindam-mazumdar/rsd-bispec","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}