Dynamical Systems Analysis of the Signed-Volume Dark Energy Model: Stability, Tracker Attractor, and Early Universe Constraints (Preprint)

In this final paper of the SV0 series, we perform a rigorous dynamical systems analysis of the signed-volume dark energy model. By introducing dimensionless variables, we recast the cosmological equations as an autonomous system of ordinary differential equations. We identify the critical points of the system and compute the eigenvalues of the Jacobian matrix to determine their stability. We demonstrate that the phantom-crossing trajectory (x = 1/2) is a stable dynamical attractor, ensuring that the model naturally evolves to the observed dark energy-dominated state. Furthermore, we analyze the early universe behavior (radiation and matter domination) and show that the exchange current is dynamically suppressed during these epochs. This suppression guarantees that the SV0 model does not disrupt the standard Big Bang Nucleosynthesis (BBN) or the formation of the Cosmic Microwave Background (CMB), establishing the model's full cosmological viability. References:[1] M. U. Sandaruwan, "Structurally Guaranteed Phantom Crossing in a Signed-Volume Effective Fluid..." (2026). Zenodo: https://doi.org/10.5281/zenodo.24026844[2] M. U. Sandaruwan, "Microphysical Origin of the Algebraic Phantom Crossing..." (2026). Zenodo: https://doi.org/10.5281/zenodo.24032977[3] M. U. Sandaruwan, "Covariant Formulation of the Signed-Volume Effective Fluid..." (2026). Zenodo: https://doi.org/10.5281/zenodo.24033838[4] M. U. Sandaruwan, "Gauge-Invariant Cosmological Perturbations in the SV0 Dark Energy Model..." (2026). Zenodo: https://doi.org/10.5281/zenodo.24034927