Testing dark-matter Euler modifications with cosmological motions: A joint RSD–lensing–gravitational-redshift analysis in an information-gauge framework

Title: Testing dark-matter Euler modifications with cosmological motions: A joint RSD–lensing–gravitational-redshift analysis in aninformation-gauge framework Submitted as a revision to Nuclear Physics B. Summary We present a phenomenological and model-agnostic framework to test whether the dark-matter velocity field obeys the standard Euler equation implied by General Relativity (GR), or exhibits effective deviations parameterized as Modified Euler (ME) dynamics. The approach combines complementary large-scale structure observables: Redshift-Space Distortions (RSD) (velocity-sensitive clustering) Weak gravitational lensing (Weyl potential ΨW= (Φ+Ψ) /2W= (+) /2ΨW= (Φ+Ψ) /2) Gravitational redshift / relativistic clustering estimators (targeting a direct potential channel Ψdir ₃₈ₑΨdir, with controlled systematics) The joint analysis enables: Consistency checks of GR in the dynamical sector (velocity–potential relation) Null tests for gravitational slip using ΨWWΨW versus Ψdir ₃₈ₑΨdir Forecasting and sensitivity projections for near-future survey combinations Contents This record includes: The full PDF of the revised manuscript (v1. 0) (figure-generation code and auxiliary files are provided in a separate Zenodo record or repository. ) Reproducibility and use The analysis is designed to be reproducible and extensible. Any code and/or scripts associated with figure generation are referenced in the manuscript and may be released separately with versioned updates. Citation If you use this material, please cite: This Zenodo record (DOI assigned by Zenodo) The associated article (journal reference to be updated upon acceptance) License Please select a license consistent with your intended reuse policy (e. g. , CC BY 4. 0 for the manuscript files, and MIT for code if released separately). Author Ju Hyung Lee