Geometric Dark Energy-Dark Matter Interactions in the SV0 Framework: Resolving the Coincidence and Instability Problems

Abstract:Interacting Dark Energy (IDE) models, where energy is exchanged between dark matter and dark energy, offer a promising solution to the cosmological coincidence problem. However, standard phenomenological IDE models often suffer from severe theoretical instabilities (such as ghost instabilities and early-time divergences) and are strongly constrained by Big Bang Nucleosynthesis (BBN). In this paper (Paper XXIX of the SV0 series), we demonstrate that the Signed-Volume (SV0) framework naturally incorporates a stable, well-behaved geometric interaction between Dark Energy and Dark Matter. We show that the interaction kernel is derived from the SV0 exchange current Q^ν, which arises from the covariant formulation (Paper III). Because the Dark Matter is identified with the Universal Information Field (UIF), the energy transfer is mediated by the logistic evolution of the two-sector volume fraction. We prove that this interaction avoids the standard early-time instabilities because the effective coupling vanishes during radiation domination (Paper V). Furthermore, the coupled dynamical equations exhibit a stable attractor that naturally drives the energy densities of Dark Energy and Dark Matter to be comparable today, thereby providing a first-principles resolution to the coincidence problem without fine-tuning.