Linear perturbation theory and structure formation in a Horndeski theory of gravity without dark matter

@misc{gervani2026linear,
  title = {{Linear perturbation theory and structure formation in a Horndeski theory of gravity without dark matter}},
  author = {Lorenzo Gervani and Antonaldo Diaferio and Francesco Pace},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.05112},
  eprint = {2611.05112},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.05112},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Linear perturbation theory and structure formation in a Horndeski theory of gravity without dark matter
AU  - Lorenzo Gervani
AU  - Antonaldo Diaferio
AU  - Francesco Pace
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.05112
UR  - https://arxiv.org/abs/2611.05112
AB  - We study the formation and evolution of the cosmic large-scale structure (LSS) in a scalar-tensor Horndeski theory of gravity without dark matter. We impose that this theory reduces to Refracted Gravity (RG) in the weak-field limit. RG is a non-relativistic theory where the gravitational permittivity ε(ρ), with ρ the baryonic matter density, provides the gravitational boost required to describe both the dynamics of galaxies and galaxy clusters without dark matter. We show that ε(ρ) equals the function G_4(φ) of the scalar field φ of our Horndeski model. The background evolution of a flat, matter-dominated, homogeneous and isotropic universe shows that φ is also responsible for the accelerated expansion of the universe and that the model is capable of reproducing the observed redshift evolution of the Hubble-Lemaître parameter. We finally develop the linear perturbation theory and study the growth factor equation. The model fails to correctly describe the LSS by predicting a late onset of the formation of cosmic structure at redshift z≲ 1.
ER  -