Abstract
We explore the cosmological consequences of having the fluctuations of the inflaton field entangled with those of another scalar, within the context of a toy model consisting of non-interacting, minimally coupled scalars in a fixed de Sitter background. We find that despite the lack of interactions in the Lagrangian, the initial state entanglement modifies the mode equation for the inflaton fluctuations and thus can induce changes in cosmological observables. These effects are examined for a variety of choices of masses and we find that they can be consistent with the requirement that the back reaction of the modified state not affect the inflationary phase while still giving rise to observable effects in the power spectrum. Our results suggest that more realistic extensions of the ideas explored here beyond the simple toy model may lead to interesting observable effects.
Highlights
UV completion, it would be difficult to make any certain assumptions about its vacuum state [3,4,5,6,7, 28]
We find that fk(0)(η), gk(0)(η) satisfy the same equation satisfied by the Bunch Davies (BD) modes and the initial conditions in eq (2.19) force fk(0)(η) = fkBD(η), gk(0)(η) = gkBD(η)
Our goal in this work was to exploit the fact that the inflaton would most likely not appear alone, but accompanied by a plethora of other scalar fields, all of which would be in
Summary
There have been a number of works on the use of Schrodinger picture field theory in inflationary settings [8,9,10], so we just describe the salient points . We will need the Hamiltonian in order to be able to set up a functional Schrodinger equation for this system. As mentioned in the introduction, at this point one might want to factor ψk into pieces only depending on φk, χk separately, since there are no cross interactions We will forgo this in order to allow for entanglement in the joint quantum state. What this means operationally is that of the two integration constants required to specify a solution of eq (2.10) only their ratio is physical We can use this freedom to specify the Wronskians W [fk, fk∗], W [gk, gk∗], which are time independent. In order for the integral to be finite, both of the eigenvalues of Ok must be positive which implies the requirement: AkRBkR − Ck2R > 0 We can rewrite this in terms of the mode functions as AkRBkR.
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