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

We study tests of the dark-matter Euler equation using a joint analysis of (i) redshift-space distortions (RSD) of galaxy clustering, (ii) weak-lensing tomographic observables of the Weyl potential, and (iii) relativistic gravitational redshift measurements that directly probe the time potential Ψ. Our starting point is a phenomenological parameterisation of non-gravitational forces and entropy-induced friction terms in the dark-matter motion law, encoded in effective functions Γ info (z, k) and θ info (z), while assuming that the metric sector obeys General Relativity with Φ = Ψ. We then show how such an effective description can arise from an information-gauge extension of ΛCDM, motivated by the Information-Gauge Renormalizable Unified Entanglement–Entropy quantum field theory (IG–RUEQFT), in which anomaly-driven entropy production and information susceptibil-ities generate the required Euler-sector terms. The resulting three-way consistency test cleanly separates “modified Euler” scenarios from modified gravity models with metric slip Φ ̸ = Ψ, constrains dark–dark and dark–baryon interactions, and explores possible links between the information sector and late-time acceleration. We present forecasts and data-driven constraints on the effective parameter set (g I , m I , χ 0 , p, θ 0 , q), identify robust signatures such as scale-dependent breaks, redshift trends, and equivalence-principle-like differential effects, and formulate null tests that can falsify this information-gauge scenario with current and upcoming large-scale-structure surveys.