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# Quantum cosmology of the open universe via closed real time path integral

Understanding the evolution of the universe through the quantum cosmologyapproach is still not fully realized yet. Introducing theBrown-Kucha$\check{\mathrm{r}}$ dust field as the time variable, we studied theevolution of the quantum universe nonperturbatively by the closed real timepath integral. We evaluated the influence functional of the massless scalarfield coupled with the flat FRW universe. By setting the initial state of thespacetime as a Gaussian wave packet, we studied the evolution of the quantumuniverse. In the proper time coordinate, if the evolution of the universe isdriven by the thermal radiation or the non-relativistic particles, we show aquantum spacetime can decohere to a classical spacetime. As the temperature ofthe thermal radiation decreases, the small quantum universe grows up to alarger classical universe. We show that whatever the form of the matter is, theclassical trajectory of the universe is always consistent with the quantumevolution of the wave packet. We find that in different scenarios, thevariation of the coherence is always consistent with the variation of the Gibbsentropy. We also studied the transition of the flat FRW universe starting fromcertain initial state of the spacetime. We illustrate that the transitionprobability is closely related to the Vilenkin's tunneling from nothingscenario. We show that the quantum universe can grow only when the initialstate of the spacetime is distributed. We also show that under the largercosmological constant or the higher radiation temperature a small universe hasa higher chance of the transition to a bigger universe. Finally, we point outthat in the proper time coordinate, the minimal coupling of the free masslessfield with the flat FRW spacetime can generally give rise to the memorycharacterized by non-Markovian correlations.

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