Quantum cosmology of a conformal multiverse

Abstract

In this paper it is studied the cosmology of a homogeneous and isotropic spacetime endorsed with a conformally coupled massless scalar field. We find six different solutions of the Friedmann equation that represent six different types of universes, all of them are periodically distributed along the complex time axis. From a classical point of view, they are then isolated, separated by Euclidean regions that represent quantum mechanical barriers. Quantum mechanically, however, there is a non-zero probability for the state of the universes to tunnel out through a Euclidean instanton and suffer a sudden transition to another state of the spacetime. We compute the probability of transition for this and other non-local processes like the creation of universes in entangled pairs and, generally speaking, in multipartite entangled states. We obtain the quantum state of a single universe within the formalism of the Wheeler-DeWitt equation and give the semiclassical state of the universes that describes the quantum mechanics of a scalar field propagating in a deSitter background spacetime. We show that the superposition principle of the quantum mechanics of matter fields alone is an emergent feature of the semiclassical description of the universe that is not valid, for instance, in the spacetime foam. We use the third quantization formalism to describe the creation of an entangled pair of universes with opposite signs of their momenta conjugated to the scale factor. Each universe of the entangled pair represents an expanding spacetime in terms of the WKB time experienced by internal observers in their particle physics experiments. We compute the effective value of the Friedmann equation of the background spacetime of the two entangled universes and, thus, the effects that the entanglement would have in their expansion rates...