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

Abstract

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.

Spinor wave function of the Universe in non-minimally coupled varying constants cosmologies

“…In such a model, both the speed of light and the gravitational constant are additional dynamic degrees of freedom represented by the two scalar fields with appropriate kinetic terms in the action. It was shown that such model includes a scenario in which the Universe is created in the process which is an analog of quantum scattering on the potential barrier [21] (this is similar to what was found in [22]), that the third quantization of the model leads to a scenario of the emergence of the multiverse from nothing [23], and that the created pairs of universes are entangled which is reflected by non-vanishing entanglement entropy [24,25]. Third quantization of slightly different models, in which the fundamental constants undergo cyclic evolution [26], yields insight into the relationship between quantum entanglement and thermodynamics [27].…”

“…Within the concept of the multiverse, there is a growing approach that regards the minisuperspace as the fundamental arena for physical phenomena to take place [22,25,28,29,31,32,33,34,35,36,37,38]. Particular models include different types of interactions between the wave functions that represent individual universes [25,31,34,35,36,37,38].…”

“…Within the concept of the multiverse, there is a growing approach that regards the minisuperspace as the fundamental arena for physical phenomena to take place [22,25,28,29,31,32,33,34,35,36,37,38]. Particular models include different types of interactions between the wave functions that represent individual universes [25,31,34,35,36,37,38]. This may suggest that a comprehensive inclusion of spin in quantum cosmology requires an application of third quantization procedure [2], in which the third-quantized action is invariant with respect to some kind of local symmetry.…”

“…As in the case of Wheeler-DeWitt equation we will use the covariance in the extended minisuperspace as guiding principle which leads to the proper form of the Dirac-Wheeler-DeWitt equation [1,2]. Since the Dirac equation without the mass term has the conformal covariance [30] we will again use (25) as the lifted metric. Thus, the covariant Dirac-Wheeler-DeWitt equation is:…”