Cosmic Void Profiles as a Visual Footprint of $\Psi$-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 $\Psi$-field cosmological theory. Using the empirical Hamaus density profile template, we evaluate how the cosmic damping mechanism ($A \approx 0.25$, $m \approx 3.0$) and the dynamic suppression of matter growth ($S_8 = 0.7460$) impact the emptiest regions of the large-scale structure. Numerical simulations demonstrate a substantial deviation from the standard $\Lambda$CDM model. In the core of cosmic voids ($R \to 0$), the standard model predicts an aggressive depletion of matter down to $-80.00\%$, whereas the $\Psi$-field architecture preserves an internal structural framework, yielding a shallower underdensity of $-71.90\%$. Furthermore, the accumulation of escaped matter at the void boundaries ($R = R_v$) 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.