When Quantum Spacetime Condenses

Constructing a self-consistent and testable theory of quantum gravity may be a key to unifying fundamental physics and understanding the dark components of the universe. In this work, we present a systematic deepening and extension of Gravitational Spinor (GS) theory, establishing a comprehensive framework that connects microscopic quantum geometry to macroscopic cosmic phenomena and opens potential pathways toward future technological applications. First, based on the principle of Generalized Gauge Equation (GGE), we construct a complete path integral (spin foam) model with Gravitational Spinor Networks (GSNs) as the state space. By intrinsically implementing the GGE constraint, we derive unique vertex amplitudes and demonstrate that the model exhibits asymptotic safety. Its core coupling constant, ${\gamma }_0$ , acts as a running parameter that flows toward an ultraviolet fixed point, ensuring the theory’s non-perturbative renormalizability. Second, we obtain classical solutions of the nonlinear GS equation, discovering stable Gravitational Condensate Stars (GCSs)—a novel class of macroscopic objects formed from nonlinear phases of spacetime geometry itself. Via a response mechanism, these solutions naturally yield Modified Newtonian Dynamics (MOND)-like behavior on galactic scales, offering a non-particle explanation for dark matter. On cosmological scales, the same mechanism induces a dynamical effective cosmological constant driven by the running of ${\gamma }_0$ , successfully accounting for the current accelerated cosmic expansion and predicting observable evolution in the dark energy equation of state. Furthermore, within the GS framework, we address several foundational puzzles: elucidating a potential mechanism for black hole information conservation through the entanglement structure of GSNs, and establishing a detailed quantitative mapping between the microscopic ${\gamma }_0\left(E\right)$ and the macroscopic phenomenological field ${\gamma }_0\left(a\right)$ . This mapping provides a concrete