Emergent Galactic Dynamics from Effective Relaxation of Baryonic Structures

This work proposes an effective, physically motivated framework for interpreting galactic-scale gravitational phenomena. Rather than introducing new fundamental degrees of freedom or modifying the underlying structure of spacetime, the model is formulated as a coarse-grained, history-dependent response of gravitational dynamics associated with the collective evolution of baryonic structures. Within this framework, gravitational dynamics include a delayed relaxation component characterized by a cosmologically determined timescale, τ = 2π/(κH), where H is the Hubble parameter. This naturally leads to an emergent acceleration scale a₀ = κcH/(2π), linking galactic dynamics to the cosmological expansion rate. We show that this framework can reproduce key empirical relations in disk galaxies, including the radial acceleration relation (RAR), galaxy rotation curves, and the baryonic Tully–Fisher relation (BTFR), without invoking non-baryonic dark matter. The results suggest that the observed acceleration scale may arise from an effective macroscopic gravitational response rather than from new fundamental components. The present work focuses on galactic-scale phenomenology. Further investigation will be required to assess consistency with gravitational lensing, galaxy clusters, and cosmological structure formation. This paper should be understood as an effective theoretical framework and not as a fundamental modification of gravity.