Fluctuations around the Wheeler-DeWitt trajectories in third-quantized cosmology

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Abstract
The effect of third quantization on Wheeler-DeWitt quantum cosmology is discussed by employing flat and open simple minisuperspace models. The wave packets are constructed based on the field-theoretical extension of the method of Hermitian invariant. These wave packets are the most ‘‘classical’’ states and evolve along the Wheeler-DeWitt trajectories, the solutions to the Wheeler-DeWitt equation, in superspace. The ‘‘observables’’ are defined by considering the universe field measurements. It is shown that the fluctuation around each Wheeler-DeWitt trajectory measured by the Heisenberg uncertainty converges on its minimum rapidly in the course of the universe expansion, while it becomes large as the scale factor approaches zero. The result suggests the importance of the description by third-quantized theory in the earliest stage of the universe.