Generating Entangled Inflationary Quantum States

Entangled inflationary quantum states offer an interesting alternative to the standard Bunch-Davies vacuum. While they can be viewed from the point of view of a theory of effective initial states, it has been unclear exactly how such states might be generated. Using a model involving two scalar fields $\Phi,\Sigma$ we show that if {\em both} fields have non-zero time dependent expectation values $\phi,\sigma$ respectively, and if the interaction potential $V(\Phi,\Sigma)$ when evaluated at these expectation values has $\partial_{\phi}\partial_{\sigma}V(\phi, \sigma)\neq 0$, this can serve as a source term for the entanglement kernel describing the state within the Gaussian approximation around the expectation values. We also show how cubic interactions between the metric perturbation $\zeta$ and a scalar $\Sigma$ can be used to generate a source term for entanglement.
Comment: 13 pages