Abstract
Within the framework of the third quantization, we consider the possibility that an initially recollapsing baby universe can enter a stage of near de Sitter inflation by tunnelling through a Euclidean wormhole that connects the recollapsing and inflationary geometries. We present the solutions for the evolution of the scale factor in the Lorentzian and Euclidean regions as well as the probability that the baby universe indeed crosses the wormhole when it reaches its maximum size.
Highlights
Classically forbidden due to their Euclidean geometry, such solutions can be traversed by means of quantum tunnelling effects and connect remote patches of the universe, or in this case the multiverse. We review how such a Euclidean wormhole appears in the third quantization treatment of a toy model of the multiverse filled by a minimally coupled massive scalar field and Galaxies 2018, 6, 19; doi:10.3390/galaxies6010019
We presented our recent results regarding the existence of Euclidean wormholes in a multiverse scenario which can connect baby and inflating universes [22]
Using the third quantization scheme, a key feature in our framework2, we were able to describe the evolution of such a multiverse in terms of the creation and annihilation of individual universes, each of them identified by the number K related to the kinetic energy of the scalar field in that particular universe
Summary
The idea that our Universe is not unique but instead resides in a collection of universes, dubbed the multiverse, has appeared several times in cosmology and within vastly different contexts, e.g., in Everett’s many worlds interpretation [1], in chaotic inflation [2,3], in the string theory landscape [4], in the ekpyrotic scenario [5,6], and many others [7,8,9,10,11,12,13,14,15]. While there is no unique precise interpretation of the term “multiverse” [9], a transversal idea is the possibility that different universes interact with each other via quantum effects. Such effects are of increased relevance in the context of the very early universe, when the energy density and curvature of the universe are expected to approach the Planck scale. Galaxies 2018, 6, 19 where homogeneity and isotropy is assumed for each sub-universe [20,22,23] This wormhole solution connects two different Lorentzian regions, one corresponding to a small recollapsing baby universe and the other corresponding to a larger asymptotically de Sitter universe. To compute the tunnelling probability, we considered the tunnelling boundary conditions introduced by Vilenkin [24,25]
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