{
  "abstract": "Matter density ($$\\rho $$) and radial pressure (p) are often used as the matter Lagrangian density ($$\\mathcal {L}_{m}$$) because both are thermodynamically consistent and produce the same Einstein field equation (EFE) in general relativity (GR). New gravity models with explicit links between matter and geometry instead involve second-order derivatives of $$\\mathcal {L}_{m}$$ relative to the metric tensor. So, picking either p or $$-\\rho $$ for $$\\mathcal {L}_{m}$$ gives different effective EFEs. This confusion appears because one usually treats the four-velocity ($$u_\\mu $$) and the metric tensor ($$g_{\\mu \\nu }$$) as independent. Here, we revisit the basics and offer a consistent framework by relaxing that assumption, thereby making the modified gravity theory independent of the choice of $$\\mathcal {L}_{m}$$. Finally, we test this approach on neutron and quark stars (ultraviolet region) and on cosmological situations with matter-dominated or dust ($$p=0$$), radiation-dominated ($$p=\\rho /3$$), and vacuum energy ($$p=-\\rho $$) equations of state (infrared region), showing how it clarifies the ambiguity in picking $$\\mathcal {L}_{m}$$ for gravity models.",
  "abstract_shown": true,
  "affiliations": [
    "Universitas Indonesia"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "B. N. Jayawiguna",
      "orcid": "0000-0001-5920-8701"
    },
    {
      "affs": [
        0
      ],
      "name": "A. Sulaksono",
      "orcid": "0000-0002-1493-5013"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4ah5arhk9cph6.bib",
  "cited_by": 0,
  "doi": "10.1140/epjc/s10052-026-16443-z",
  "fulltext_url": null,
  "id": "4ah5arhk9cph6",
  "issns": [
    "1434-6052"
  ],
  "landing_url": "https://link.springer.com/article/10.1140/epjc/s10052-026-16443-z",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0",
  "metadata_licence": null,
  "native_subjects": [
    [
      "feed-journal",
      "physics/high-energy"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://link.springer.com/content/pdf/10.1140/epjc/s10052-026-16443-z.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": "Springer Science and Business Media LLC",
  "ris": "https://research.draconitic.com/paper/4ah5arhk9cph6.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:19Z",
      "native_id": "10.1140/epjc/s10052-026-16443-z",
      "source": "feed-springer",
      "url": "https://link.springer.com/article/10.1140/epjc/s10052-026-16443-z"
    },
    {
      "first_seen": "2026-11-03T12:20:29Z",
      "native_id": "10.1140/epjc/s10052-026-16443-z",
      "source": "crossref",
      "url": "https://link.springer.com/article/10.1140/epjc/s10052-026-16443-z"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "feed-journal:physics/high-energy",
      "subfield": "high-energy"
    }
  ],
  "title": "Ambiguity in matter sector for modified gravity involving $$\\delta ^2 \\mathcal {L}_{m}/\\delta g^{\\mu \\nu }\\delta g^{\\alpha \\beta }$$ and its implications to astrophysics and cosmology",
  "title_text": "Ambiguity in matter sector for modified gravity involving δ ^2 ℒ_m/δ g^μ ν δ g^α β  and its implications to astrophysics and cosmology",
  "type": "peer-reviewed",
  "updated_at": "2026-11-05T00:20:42Z",
  "url": "https://research.draconitic.com/paper/4ah5arhk9cph6",
  "venue": "The European Physical Journal C",
  "versions": []
}