Dynamical Dimensional Phase Transition via Null State Instability: A Non-Singular Origin of the Universe

We propose a self-consistent cosmological framework where spacetime dimensionality is not a fixed background but a dynamical scalar field D(xμ) governing the topological unfolding of the universe. By redefining the pre-Big Bang state as a "Null State" (D≈0), we identify a metastable false vacuum characterized by maximal symmetry and high potential energy. We demonstrate mathematically that this state possesses a tachyonic instability (V^{}<0), which triggers a Dynamical Dimensional Phase Transition (DPT). This mechanism resolves the classical initial singularity problem inherent in General Relativity by replacing the geometric t=0 point with a quantum topological phase transition. Furthermore, we derive the effective action for the dimensional field via the Coleman-De Luccia instanton mechanism and discuss observational signatures in the stochastic gravitational wave background (SGWB). The model predicts a specific power-law spectrum ΩGW(f)∝ f³ in the infrared tail, providing a falsifiable prediction for future space-based interferometers such as LISA and DECIGO.