  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...
