{
  "abstract": "The correlation dimension ($D_2$) provides a scale-dependent characterization of the transition towards homogeneity and a complementary perspective on the clustering of large-scale structure. In this work, we study its full dependence on scales and redshift connecting $D_2$ directly to the matter power spectrum of a given cosmological model, and derive an approximate analytical relation based on an effective cut-off representation of the filtering kernel. We further perform two complementary local (derivative-based) and global (variance-based) sensitivity analyses within the $w_0w_a$CDM model. In general, nonlinear evolution lowers $D_2$ relative to the linear prediction at small scales, with the effect becoming more pronounced at low redshift. Our cut-off approximation, with $k_{\\rm cut}=α/r$ and $α\\simeq 2.39$, reproduces the exact $D_2$ to better than 1\\% for the representative cases considered. The sensitivity analysis identifies $Ω_m$ and $A_s$ as the dominant parameters for the linear correlation dimension and its nonlinear-to-linear ratio, respectively, while $w_0$ and $w_a$ induce scale- and redshift-dependent changes in the nonlinear contribution. These results provide a framework for characterizing the cosmological scale- and redshift-dependent features of $D_2$ and its nonlinear correction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39867",
  "author_total": 2,
  "authors": [
    {
      "name": "Miguel Aparicio Resco"
    },
    {
      "name": "Florencia A. Teppa Pannia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2jhggtp5c66tc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39867",
  "fulltext_url": null,
  "id": "2jhggtp5c66tc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39867",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "astro-ph.CO"
    ],
    [
      "openalex",
      "3103|Cosmology and Gravitation Theories"
    ]
  ],
  "openalex": "W7215094828",
  "pdf_url": "https://arxiv.org/pdf/2609.39867",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2jhggtp5c66tc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39867",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39867"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.CO",
      "subfield": "cosmology"
    }
  ],
  "title": "The Cosmological Correlation Dimension Beyond the Linear Regime: Analytical Approximation and Parameter Sensitivity",
  "title_text": "The Cosmological Correlation Dimension Beyond the Linear Regime: Analytical Approximation and Parameter Sensitivity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/2jhggtp5c66tc",
  "venue": "arXiv",
  "versions": []
}