Quantum cosmology of a conformal multiverse

Abstract

This paper studies 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, and 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 nonzero 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 nonlocal 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 de Sitter 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 the momentum conjugated to the scale factor. Each universe of the entangled pair represents an expanding spacetime in terms of the Wentzel-Kramers-Brillouin (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 effect that the entanglement would have in their expansion rates. We analyze as well the effects of the interuniversal entanglement in the properties of the scalar fields that propagate in each spacetime of the entangled pair. We find that the largest modes of the scalar field are unaware of the entanglement between the universes, but the effects can be significant for the lowest modes, allowing us to compute, in principle, detailed observational imprints of the multiverse in the properties of a single universe like ours.

Singularities and Cyclic Universes

“…All this is in agreement with the claim that macroscopic quantum effects in cosmology are possible [14]. In a more recent contribution [15] it has been shown that within the framework of third quantization picture, where one defines creation and annihilation operators as in quantum field theory one is able to consider parallel evolving universes as a pair of spontaneously created from the vacuum state remaining quantum mechanically entangled during their classical evolution. An interesting effect is that for such a pair the entropy of entanglement is also large at the maximum point of expansion presumably signalling strong quantum effects there.…”

Time Reversal Symmetry in Cosmology and the Creation of a Universe–Antiuniverse Pair

“…In this paper we review and gather the main results of previous works [2,3,[8][9][10] and extend the hypothesis presented in [11] for the restoration of the primordial matter-antimatter asymmetry to the more general scenario of two homogeneous and isotropic pieces of the spacetime whose time variables are, according to the time reversal symmetry of the Einstein-Hilbert action, reversely related. That will prepare the arena for more detailed, future developments on the subject.…”

“…where n (1) k are the particles in the mode k created in one of the universes, labeled as 1, and n (2) k are the particles in the mode k created in the other universe, labeled as 2. For the inhabitants of the two universes the primordial antimatter is essentially created in the partner universe, i.e.…”

“…For the inhabitants of the two universes the primordial antimatter is essentially created in the partner universe, i.e. for an observer in the universe 1, n (2) k are the antiparticles that she misses in her universe and, analogously, n (1) k are the antiparticles in the mode k that are left from the point of view of an observer of the universe 2. Particles and antiparticles cannot interact, and therefore cannot annihilate each other, because the Euclidean gap (a quantum barrier) that separates the universes (see Fig.…”

“…However, the analysis of the emergence of the classical spacetime in quantum cosmology suggests that the time variables of the two universes should be reversely related [2,3], t 1 = −t 2 . In that case, the matter that propagates in one of the universes can naturally be identified, from the point of view of the symmetric universe, with antimatter, and viceversa.…”