Scale-Dependent Weak-Field Dynamics in Horndeski Theory: Galaxy Rotation Curves and Turnaround Scales

Abstract

In this work, the weak-field dynamics of a gravitational-wave compatible subclass of Horndeski gravity is investigated on galactic and intergalactic scales. The analysis is performed within the weak-field approximation for stationary and approximately spherically symmetric configurations, retaining the nonlinear scalar derivative interactions responsible for scale-dependent modifications of the gravitational field. On galactic scales, the transition regime is investigated through the effective potential, the stability of circular orbits, galaxy rotation curves, and the relation between dynamical and lensing masses. The analysis shows that the scalar field modifies the orbital dynamics and the radial dependence of the rotational velocity, while generating a nonvanishing gravitational slip between the dynamical and lensing mass estimates. On intergalactic scales, the asymptotic weak-field dynamics is investigated and a turnaround scale is derived from the balance between the effective gravitational attraction and the large-scale curvature contribution. At large distances, the asymptotic gravitational field is governed by the background curvature contribution.