Mercury (Hg): a relativistic N-body simulation for Horndeski gravity
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 αK, αB, αM, αT 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.
Related
- Horndeski Gravity as an Effective Dark Energy Fluid in Cosmological N-body Simulations
- Linear perturbation theory and structure formation in a Horndeski theory of gravity without dark matter
- Constraints on Horndeski gravity with phantom crossing
- Constraints on Horndeski gravity with phantom crossing
- Nonreciprocal black holes with primary hair in beyond Horndeski gravity: Exact solutions and stability
BibTeX
@misc{nourizonoz2026mercury,
title = {{Mercury (Hg): a relativistic $N$-body simulation for Horndeski gravity}},
author = {Ahmad Nouri-Zonoz and Farbod Hassani and Julian Adamek and Emilio Bellini and Martin Kunz},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03637},
eprint = {2611.03637},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03637},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Mercury (Hg): a relativistic N-body simulation for Horndeski gravity
AU - Ahmad Nouri-Zonoz
AU - Farbod Hassani
AU - Julian Adamek
AU - Emilio Bellini
AU - Martin Kunz
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03637
UR - https://arxiv.org/abs/2611.03637
AB - 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_K, α_B, α_M, α_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.
ER -