Abstract
In this work, we investigate the quantum effects of relic gravitons from a Schrödinger-picture point of view. By considering the gravity-wave equations in the Friedmann–Robertson–Walker cosmological background, we reduce the problem to that of a generalized time-dependent harmonic oscillator and find the corresponding exact analytic wave functions with the help of the dynamical invariant operator method. Afterward, we derive the geometric phases and squeezed quantum states for this system. We also evaluate the quantum fluctuations and the uncertainty product for each mode of the quantized field.
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