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The effects of the entanglement of the inflaton field which initially entangled with those of another field on observables like power spectrum are known in the context of the SchrÃ¶dinger field theory. To clarify this effect in the Heisenberg picture, there were some attempts to construct the initial entangled state by making use of an entangled transformation (like Bogoliubov transformation) between the Bunch-Davies vacuums and squeezed states. We study the role of the time-dependent entangled transformation in the SchrÃ¶dinger field theory. We derive the relation between two vacuum states which their mode functions are transformed by the entangled transformation in SchrÃ¶dinger picture. We discuss that the time-dependency of the entanglement parameter is inevitable and only in the first order of the entanglement parameter perturbation this time-dependency vanishes. We study the entangled transformation in the Heisenberg picture in term of the entangled parameter which appears in the entangled state in SchrÃ¶dinger picture.
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