{"paper":{"title":"The Fluctuation Theory, Critical Phenomena and Gravitational Clustering of Galaxies","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Azmat Khan, Farooq Owais, M. H. Abdullah, M. S. Khan, Shah Zahir","submitted_at":"2025-08-06T09:20:25Z","abstract_excerpt":"We investigate the phenomenon of clustering of galaxies in an expanding universe by applying the fluctuation theory. We evaluate the fluctuation moments for the number of particles and the correlated fluctuations for number and energy of particles, clustering under their mutual gravitation. The correlated fluctuations $<\\Delta N\\Delta U>$ show that the value of $<\\Delta N>$ can be both positive as well as negative, because it is the difference between $N$ and the mean value of $N$. A negative $<\\Delta N>$ corresponds to regions of under density and positive $<\\Delta N>$ corresponds to regions "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.04237","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.04237/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}