Cosmic Void Profiles as a Visual Footprint of Ψ-Field Gravity: Mitigation of Underdensity Depletion and the Soft-Ridge Phenomenon

We explore the dynamics and morphology of cosmic voids within the framework of the modified Ψ-field cosmological theory. Using the empirical Hamaus density profile template, we evaluate how the cosmic damping mechanism (A ≈ 0.25, m ≈ 3.0) and the dynamic suppression of matter growth (S₈ = 0.7460) impact the emptiest regions of the large-scale structure. Numerical simulations demonstrate a substantial deviation from the standard ΛCDM model. In the core of cosmic voids (R → 0), the standard model predicts an aggressive depletion of matter down to $-80.00%$, whereas the Ψ-field architecture preserves an internal structural framework, yielding a shallower underdensity of $-71.90%$. Furthermore, the accumulation of escaped matter at the void boundaries (R = Rᵥ) is significantly suppressed, reducing the sharp density ridge from $+5.74%$ down to a smoother $+5.51%$. This "soft-ridge" phenomenon represents a direct geometric consequence of the field's internal moisture, which provides an isotropic resistance against rapid dark matter evacuation. These distinct structural modifications offer a pristine, testable signature for upcoming deep-space wide-field surveys, such as the Euclid satellite and the Vera C. Rubin Observatory.