{"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/large-scale-structure-of-the-universe-and","title":"Large-Scale Structure of the Universe and Cosmological Perturbation Theory","arxiv_id":"astro-ph/0112551","date":"2001-12-27","proceeding":null,"authors":["F. Bernardeau","S. Colombi","E. Gaztanaga","R. Scoccimarro"],"abstract":"We review the formalism and applications of non-linear perturbation theory (PT) to understanding the large-scale structure of the Universe. We first discuss the dynamics of gravitational instability, from the linear to the non-linear regime. This includes Eulerian and Lagrangian PT, non-linear approximations, and a brief description of numerical simulation techniques. We then cover the basic statistical tools used in cosmology to describe cosmic fields, such as correlations functions in real and Fourier space, probability distribution functions, cumulants and generating functions. In subsequent sections we review the use of PT to make quantitative predictions about these statistics according to initial conditions, including effects of possible non Gaussianity of the primordial fields. Results are illustrated by detailed comparisons of PT predictions with numerical simulations. The last sections deal with applications to observations. First we review in detail practical estimators of statistics in galaxy catalogs and related errors, including traditional approaches and more recent developments. Then, we consider the effects of the bias between the galaxy distribution and the matter distribution, the treatment of redshift distortions in three-dimensional surveys and of projection effects in angular catalogs, and some applications to weak gravitational lensing. We finally review the current observational situation regarding statistics in galaxy catalogs and what the future generation of galaxy surveys promises to deliver.","url_abs":"https://arxiv.org/abs/astro-ph/0112551v1","url_pdf":"https://arxiv.org/pdf/astro-ph/0112551v1.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":"abstracts"},"code_links":[{"paper_slug":"large-scale-structure-of-the-universe-and","repo_url":"https://github.com/lhd23/RSDPT-FFTLog","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=astro-ph%2F0112551","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"astro-ph/0112551"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/lhd23/RSDPT-FFTLog","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"unverified":3},"by_repo_kind":{"listed":{"samples":3,"ran":0,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"de2c883c0330764e","entry":"cut_off_ringing","repo":"lhd23/RSDPT-FFTLog","repo_kind":"listed","path":"power_FFTLog.py","file_url":"https://github.com/lhd23/RSDPT-FFTLog/blob/HEAD/power_FFTLog.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"de2c883c0330764e"}},{"code_sha256_prefix":"12eeeb2eaa37d38a","entry":"get_fftlog_param_dict","repo":"lhd23/RSDPT-FFTLog","repo_kind":"listed","path":"pars.py","file_url":"https://github.com/lhd23/RSDPT-FFTLog/blob/HEAD/pars.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"12eeeb2eaa37d38a"}},{"code_sha256_prefix":"7517b445ccc7a8af","entry":"my_logspace","repo":"lhd23/RSDPT-FFTLog","repo_kind":"listed","path":"FFTLog_integrals.py","file_url":"https://github.com/lhd23/RSDPT-FFTLog/blob/HEAD/FFTLog_integrals.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"7517b445ccc7a8af"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}