Abstract
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 Schr\"odinger 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 Schr\"odinger field theory. We derive the relation between two vacuum states which their mode functions are transformed by the entangled transformation in Schr\"odinger 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 Schr\"odinger picture.
Highlights
The main experimental observation of the early universe, cosmic microwave background (CMB), have become very accurate and have allowed us to deduce the details of the even earlier phase of the cosmos [1]
An important aspect of the quantum physics is the entanglement which can have the observational effect on cosmic structure formation which has originated from quantum fluctuations in the early universe [5]
People do not have a detailed description of this process, so they just resort to a phenomenological framework that considers the EFT comes up with a slightly more general form of the wave function than Bunch-Davies. Another point of view is that we are embracing hints from the data that there may be a small breaking of rotational invariance in the state of the universe, and are considering a simple extension of BunchDavies that allows for this kind of breaking
Summary
The main experimental observation of the early universe, cosmic microwave background (CMB), have become very accurate and have allowed us to deduce the details of the even earlier phase of the cosmos [1]. Apart from this fact that the Heisenberg picture field theory is more common and easier to study the inflationary models (for example the calculation of the Power spectrum and non-Gaussianity in the Schrödinger picture needs the heavy calculation on the functional space), this picture has better description for particle representation of each state with explicit presentation of annihilation and creation process. We show that though Kanno [15] presented a novel way to study the entangled state in the Heisenberg picture, her calculation and analysis to introduce the entanglement was not correct in some parts. We follow her way to study the role of the time-dependent entangled transformation in the Schrödinger field theory.
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