Integrated collective dynamics: A purely theoretical scalar-tensor framework for gravitational dynamics without dark components

We propose Integrated Collective Dynamics (ICD), a novel scalar-tensor theory inspired by emergent phenomena in complex systems, to provide a unified, purely theoretical framework for gravitational dynamics across galactic and cosmological scales without invoking dark matter or dark energy. Integrated Collective Dynamics conceptualizes gravitational systems as ensembles of interacting particles, where collective interactions, mediated by a massive scalar field, produce emergent modifications to gravity. In the Newtonian limit, Integrated Collective Dynamics employs a rigorously derived correction function to reproduce flat galactic rotation curves, eliminating the need for dark matter through a statistical mechanics-inspired approach. Relativistically, we formulate Integrated Collective Dynamics as a scalar-tensor theory with a meticulously constructed action, deriving field equations via variational principles and solving them analytically in various regimes. The scalar field naturally induces cosmic acceleration, supplanting dark energy, and predicts qualitative modifications to gravitational lensing, the cosmic microwave background, and structure formation. New additions include quantitative predictions for rotation curves, comparisons with alternative theories, and discussions of model limitations. These predictions, grounded in perturbation theory, asymptotic analysis, and rigorous mathematical derivations, highlight Integrated Collective Dynamics's potential to reshape our understanding of gravity. Rooted in field theory and statistical mechanics, Integrated Collective Dynamics offers a mathematically elegant alternative to the ΛCDM paradigm, addressing fundamental questions about the microscopic origins of gravity and its potential unification with quantum mechanics.