HγC VIII: Void Dynamics and Structure Formation in Relational Accumulation Cosmology

We investigate structure formation in relational accumulation cosmology by focusing on the dynamics of accumulation fluctuations in underdense environments. Building on the background cosmological evolution of the accumulation field developed in earlier work, we consider a minimal fluctuation equation including baryonic sourcing, damping, and diffusion. This provides a phenomenological framework in which the growth and redistribution of accumulation fluctuations can be studied across different cosmic environments. In underdense regions, baryonic sourcing is reduced relative to the cosmic mean. We show that this leads to a systematic suppression and smoothing of accumulation fluctuations, with characteristic dependence on spatial scale and cosmic epoch. However, the effective gravitational response is not determined directly by the sign of the density contrast. Instead, it is governed by the spatial profile of the accumulation field, implying that void dynamics must be understood in terms of profile-dependent accumulation response rather than matter deficit alone. Cosmic voids therefore provide a particularly clean regime in which the interplay between reduced sourcing, damping, and diffusion can be isolated. Within this setting, the accumulation framework predicts an environment-dependent weakening of the effective gravitational response and a corresponding modification of structure-formation phenomenology relative to standard matter-based descriptions. The present analysis is qualitative and intended as a proof of principle. Its purpose is to establish the basic phenomenology of accumulation fluctuations in underdense environments and to identify cosmic voids as a natural testing ground for relational accumulation cosmology.