{
  "abstract": "We present a joint observational analysis confronting viable $f(R)$ modified gravity theories, specifically the Hu \\& Sawicki and Starobinsky models, with background and large-scale structure (LSS) data. Utilizing Monte-Carlo Markov chain (MCMC) sampling across datasets including baryon acoustic oscillations (BAO), type Ia supernovae (SNeIa), cosmic microwave background (CMB) distance priors, and linear growth measurements ($fσ_8$, $f$, $σ_8$), we place tight constraints on the model parameters governing deviations from General Relativity. For the full dataset combination, we obtain $\\log_{10} b_\\mathrm{HS} = -6.325_{-1.138}^{+1.216}$ for the Hu \\& Sawicki model and $b_\\mathrm{S} = (0.8\\pm61.0)\\times10^{-4}$ for the Starobinsky model. Model comparison based on the Akaike Information Criterion indicates that these $f(R)$ extensions are statistically favored over flat $Λ\\text{CDM}$ ($|Δ\\text{AIC}| \\ge 3.99$) for the combined data. However, when considering the Bayesian Information Criterion, the evidence for support is significantly reduced. Furthermore, we construct two-dimensional phase-space diagrams in the $(μ, γ)$ and $(μ, Σ)$ planes across several redshifts, establishing a novel diagnostic null-test allowing us to probe for deviations from $Λ\\text{CDM}$, corresponding to the fixed point $(1,1)$ in both planes, using LSS observables. Should future weak-lensing and galaxy surveys provide data points with $μ-1<0$ and $γ-1>1$ or $Σ-1 < 0 $, then the aforementioned models could be directly ruled out.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10651",
  "author_total": 3,
  "authors": [
    {
      "name": "Tshepo Mathibela"
    },
    {
      "name": "Alvaro de la Cruz-Dombriz"
    },
    {
      "name": "Savvas Nesseris"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3aqm90bm9znpd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10651",
  "fulltext_url": null,
  "id": "3aqm90bm9znpd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10651",
  "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",
      "physics.gen-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.10651",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3aqm90bm9znpd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:26Z",
      "native_id": "2609.10651",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10651"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.gen-ph",
      "subfield": "general"
    }
  ],
  "title": "Constraining $f(R)$ gravity and evolving dark energy via large-scale structure and phase-space trajectories",
  "title_text": "Constraining f(R) gravity and evolving dark energy via large-scale structure and phase-space trajectories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:26Z",
  "url": "https://research.draconitic.com/paper/3aqm90bm9znpd",
  "venue": "arXiv",
  "versions": []
}