Quantum cosmology of the flat universe via closed real-time path integral

Abstract

Understanding the evolution of the universe through the quantum cosmology approach is still not fully realized yet. Introducing the Brown-Kuchař dust field as the time variable, we studied the evolution of the quantum universe nonperturbatively by the closed real time path integral. We evaluated the influence functional of the massless scalar field coupled with the flat FRW universe. By setting the initial state of the spacetime as a Gaussian wave packet, we studied the evolution of the quantum universe. In the proper time coordinate, if the evolution of the universe is driven by the thermal radiation or the non-relativistic particles, we show a quantum spacetime can decohere to a classical spacetime. As the temperature of the thermal radiation decreases, the small quantum universe grows up to a larger classical universe. We show that whatever the form of the matter is, the classical trajectory of the universe is always consistent with the quantum evolution of the wave packet. We find that in different scenarios, the variation of the coherence is always consistent with the variation of the Gibbs entropy. We also studied the transition of the flat FRW universe starting from certain initial state of the spacetime. We illustrate that the transition probability is closely related to the Vilenkin's tunneling from nothing scenario. We show that the quantum universe can grow only when the initial state of the spacetime is distributed. We also show that under the larger cosmological constant or the higher radiation temperature a small universe has a higher chance of the transition to a bigger universe. Finally, we point out that in the proper time coordinate, the minimal coupling of the free massless field with the flat FRW spacetime can generally give rise to the memory characterized by non-Markovian correlations.