P-10: The Geometric Origin of Cosmic Lifetime — From Space Micro-elements to Trillions of Years

Abstract:How much longer can the universe exist? The standard cosmological model (ΛCDM) determines the ultimate fate of the universe using a "cosmological constant" Λ whose physical origin is obscure, giving rise to the notorious "fine-tuning problem" and "coincidence problem." Based on Space Ontology, we rigorously prove that the universe is not a cold machine governed by external constants, but a self-contained, living geometry governed by its sole free parameter κ=0.017. Starting from the Hamiltonian of Planck vortex micro-elements, we prove that energy conservation of the entire universe as an isolated system is an inevitable consequence of geometric dynamics. On this basis, we reveal that dark matter and dark energy are not two independent entities, but different phases of an ongoing slow phase transition of spatial vortices. From the unified action, we rigorously derive the resonant conversion rate ̄Γ/H₀ = 0.0115 ± 0.0015 from dark matter to dark energy, and by solving the self-consistent coupled evolution equations, we obtain the cosmic lifetime t_life ≈ 1.2 × 10¹² years (1.2 trillion years). We further predict that this phase transition leaves observable imprints in the night sky today: the dark energy equation of state w(z) will exhibit a characteristic oscillation around z∼0.5, and the Hubble parameter H(z) will be slightly higher than expected from the standard cosmological model. We also find that the ratio between the current age of the universe (13.8 billion years) and the time it has left (1.2 trillion years) is the profound number 87—directly arising from the conversion rate ̄Γ/H₀, uniquely determined by κ=0.017. Finally, we reveal the deep geometric connection between Avogadro's constant and the cosmic lifetime: the former is the characteristic number of nucleons for the transition from "negative-pressure confinement" to "freedom" in the microscopic world, while the latter is the characteristic time for the transition from "vortex condensation" to "equilibrium dispersion" in the cosmic world. Both originate from the same root, κ=0.017. This paper is the tenth in the first series (17 papers total) of Space Ontology, establishing the geometric origin of cosmic lifetime from space micro-elements to trillions of years.