Decaying universes and the emergence of Bell-type interuniversal entanglement in varying fundamental constants cosmological model

In this paper, we consider a high-curvature limit of the varying fundamental constants toy model in which both the value of the speed of light and the value of the gravitational constant are related to the values of the two non-minimally coupled scalar fields. The high-curvature limit motivates the application of the third quantization procedure to such a toy model which results in a theory that describes bosonic massive particles that move freely in the three-dimensional minisuperspace associated with the degrees of freedom of the original model. Motivated by the idea that in the quantum cosmological description the minisuperspace gets promoted to a real configurational space of the system we supplement the third quantized action of the considered model with an interaction term that allows for decay and scattering processes. We show that such interaction term induces a scenario in which a parent universe decays into two universes described by a nearly maximally entangled Bell state. We eventually asses the strength of the entanglement, in the created pair of universes, by calculating the von Neumann entropy of entanglement.