Damped Harmonic Gravity (DHG) formalism: A unified approach to galactic dynamics and cluster cohesion without dark matter.

A unified approach to galactic dynamics and cluster cohesion without dark matter. This document presents the Damped Harmonic Gravity (DHG) model, a phenomenological extension of Newtonian dynamics proposing that the gravitational potential undergoes harmonic modulation resulting from the intrinsic impedance of the vacuum. Unlike models of particle dark matter or monolithic modifications of Newton's law, the DHG model introduces an effective oscillatory potential defined by a spatial wavelength (λ=25 kpc) and an exponential attenuation factor (γ = 0.03 kpc⁻¹). We demonstrate that this resonant coupling (α = 1.2) makes it possible to explain the flat rotation curves of spiral galaxies by generating a "boost" of apparent dynamic mass which can reach 110% at the paroxysm of the wave (~10.5 kpc), while remaining undetectable on the scale of the Solar System where the acceleration remains above the critical threshold (a0 = 1.2.10-10 m/s2). Extending the model to a second harmonic (λ2 = 250 kpc) offers a robust solution to the velocity dispersion paradox in galaxy clusters, predicting structural cohesion consistent with historical Zwicky observations without the addition of exotic mass. Finally, we discuss the cosmological implications of the model, suggesting that the accelerated expansion of the Universe could be a manifestation of harmonic vacuum pressure on very large scales. The DHG model thus provides a unified framework, testable by future precision data from the Gaia satellite, for linking particle physics to the large-scale structure of space-time