An empirically constrained Covariant Modified Gravity: exact reconstruction of galactic rotation curves and lensing
Abstract
We present a covariant modified gravity theory which reproduces all the galactic phenomenology usually attributed to dark matter in the low acceleration regime, including the flat rotation curves of massive tracers, and the deflection angles of photons as inferred through gravitational lensing. We first derive a fully covariant description of galactic space-times under a spherically symmetric and static approximation. This description accounts for flat rotation curves, observed gravitational lensing phenomenology and the Tully-Fisher mass scalings of the above. The resulting covariant description is then used to constrain the parameters of a minimally coupled gravitational action using power laws for both the Ricci scalar and the matter Lagrangian. The action presented hence leads to field equations whose trace, under the approximations taken, has as solutions metric coefficients which exactly reproduce flat rotation curves, gravitational lensing observations and observationally determined Tully-Fisher galactic mass scalings of any required index. This last allowing for an accurate fitting of observational dynamics up to galaxy cluster scales.
Related
- Black Hole Spacetime Reconstruction from Galactic Rotation Curves: Thermodynamic Properties and Implications
- Single-Parameter Exponential Model Outperforms Standard Dark Matter and Modified Newtonian Frameworks in Predicting Galactic Rotation Curves
- Thermodynamic reconstruction in observationally constrained dynamical dark energy models
- GRAVITY-RESOLVE: A comprehensive image reconstruction tool for Galactic Center observations with GRAVITY
- A unified cosmographic reconstruction of the Hubble expansion: Bayesian constraints on dark energy and modified-gravity diagnostics
BibTeX
@misc{hernandez2026empirically,
title = {{An empirically constrained Covariant Modified Gravity: exact reconstruction of galactic rotation curves and lensing}},
author = {Xavier Hérnandez and Sergio Mendoza and Sarahí Silva and Edgar Gasperín},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20865},
eprint = {2609.20865},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20865},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An empirically constrained Covariant Modified Gravity: exact reconstruction of galactic rotation curves and lensing
AU - Xavier Hérnandez
AU - Sergio Mendoza
AU - Sarahí Silva
AU - Edgar Gasperín
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.20865
UR - https://arxiv.org/abs/2609.20865
AB - We present a covariant modified gravity theory which reproduces all the galactic phenomenology usually attributed to dark matter in the low acceleration regime, including the flat rotation curves of massive tracers, and the deflection angles of photons as inferred through gravitational lensing. We first derive a fully covariant description of galactic space-times under a spherically symmetric and static approximation. This description accounts for flat rotation curves, observed gravitational lensing phenomenology and the Tully-Fisher mass scalings of the above. The resulting covariant description is then used to constrain the parameters of a minimally coupled gravitational action using power laws for both the Ricci scalar and the matter Lagrangian. The action presented hence leads to field equations whose trace, under the approximations taken, has as solutions metric coefficients which exactly reproduce flat rotation curves, gravitational lensing observations and observationally determined Tully-Fisher galactic mass scalings of any required index. This last allowing for an accurate fitting of observational dynamics up to galaxy cluster scales.
ER -