Eternal Quantum Universe

Title: Eternal Quantum Universe

Author: Ding Jia

Abstract: In an eternal classical universe, a spacetime extends indefinitely in time. In an eternal quantum universe, all spacetimes in superposition extend indefinitely in time. The latter scenario can be realized by a unimodular path integral in the limit of infinite four-volume (assuming finite spatial volumes). Since the spacetime volume is fixed, the path integral kernel obeys the Schrödinger instead of the Wheeler-DeWitt equation. Since the boundaries recede to infinity, only Hamiltonian eigenstates and their mixtures form well-defined boundary conditions. Given the time-invariant boundary states, the familiar picture of an evolving universe only appears through the imposition of interior conditions to describe local observations. Due to the Lorentzian constraint, the saddle points extend beyond spacetime singularities to eternity. In this scenario, the universe has no beginning or ending in both quantum and classical-effective settings.

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• Article v1.0: original version