{
  "abstract": "We present Mercury, a relativistic $N$-body code for cosmological simulations in the $α$-basis formulation of Horndeski gravity. Mercury extends a particle-mesh scheme by incorporating the dynamics of the additional scalar degree of freedom and the corresponding modified Einstein equations, expressed in terms of the time-dependent functions $α_{\\rm K}, α_{\\rm B}, α_{\\rm M}, α_{\\rm T}$ and the effective Planck mass $M_*^2$. This generalises our previous implementation of Horndeski subclass models, namely $k$-essence and kinetic gravity braiding (KGB), to the general linear Horndeski $α$-basis. The code evolves the additional scalar degree of freedom and its effective stress--energy tensor alongside the nonlinear matter and metric fields, so that nonlinear structure formation sources the scalar-field evolution and feeds back on the gravitational potentials. Through its interface with hi_class, Mercury supports both phenomenological $α$-function parametrisations and covariant Horndeski theories; we demonstrate the latter using nKGB, the Cubic Galileon, and Brans--Dicke models. We validate the implementation against hi_class in the linear regime and recover the expected nonlinear $k$-essence and KGB limits. For the luminal Horndeski models considered here, we show how a running effective Planck mass generates gravitational slip through the scalar anisotropic stress and modifies the friction terms governing the vector and tensor metric perturbations. The evolution of $M_*^2$ also modifies the normalisation and scale dependence of the effective dark-energy density contrast, leaving a corresponding imprint on its power spectrum. The present framework provides an intermediate step towards nonlinear Horndeski simulations, in which nonlinear scalar self-interactions and screening effects can be incorporated consistently within the same relativistic framework.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03637",
  "author_total": 5,
  "authors": [
    {
      "name": "Ahmad Nouri-Zonoz"
    },
    {
      "name": "Farbod Hassani"
    },
    {
      "name": "Julian Adamek"
    },
    {
      "name": "Emilio Bellini"
    },
    {
      "name": "Martin Kunz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fnw27pa4bbrdb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03637",
  "fulltext_url": null,
  "id": "fnw27pa4bbrdb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03637",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "astro-ph.CO"
    ],
    [
      "arxiv",
      "gr-qc"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03637",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fnw27pa4bbrdb.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:04Z",
      "native_id": "2611.03637",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03637"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.CO",
      "subfield": "cosmology"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Mercury (Hg): a relativistic $N$-body simulation for Horndeski gravity",
  "title_text": "Mercury (Hg): a relativistic N-body simulation for Horndeski gravity",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:21Z",
  "url": "https://research.draconitic.com/paper/fnw27pa4bbrdb",
  "venue": "arXiv",
  "versions": []
}