What if? Exploring the multiverse through Euclidean wormholes

Abstract

We present Euclidean wormhole solutions describing possible bridges within the multiverse. The study is carried out in the framework of third quantisation. The matter content is modelled through a scalar field which supports the existence of a whole collection of universes. The instanton solutions describe Euclidean solutions that connect baby universes with asymptotically de Sitter universes. We compute the tunnelling probability of these processes. Considering the current bounds on the energy scale of inflation and assuming that all the baby universes are nucleated with the same probability, we draw some conclusions about which universes are more likely to tunnel and therefore undergo a standard inflationary era.

The Third Quantization: To Tunnel or Not to Tunnel?

“…Thus, the possibility arises for a baby universe to quantum tunnel through the wormhole and emerge as an inflating universe. We summarize the results of our recent paper [22], presenting the explicit solutions for the evolution of the scale factor in the two Lorentzian and the Euclidean regions as well as showing how the tunnelling probability varies with the inflationary scale and the momentum of the scalar field. To compute the tunnelling probability, we considered the tunnelling boundary conditions introduced by Vilenkin [24,25].…”

“…During the expanding phase, the analytical solution a(η), where η is the conformal time defined by dη = a −1 dt, was obtained for the first time in [22] and reads…”

“…As in the previous case, a solution for a(η) was obtained in [22] in terms of Jacobi elliptic functions sn(u|m) and cn(u|m) [28]:…”

“…By quantizing the wave function of the spacetime and matter fields, which satisfies a possibly non-linear Wheeler-DeWitt equation, and defining creation and annihilation operators of individual universes with a particular spacetime-matter configuration, the third quantization treats the multiverse as a quantum system of particles (universes) with interactions (topology changes) [19,20]. At the semiclassical level, these interactions are often associated to the existence of Euclidean wormholes or instantons, which where first considered in the decay process of a false vacuum [21] (for further works on Euclidean wormholes and instantons in various contexts, please check the references cited in [22]). Although classically forbidden due to their Euclidean geometry, such solutions can nevertheless be traversed by means of quantum tunnelling effects and therefore connect remote patches of the universe, or in this case the multiverse.…”

“…In this work, 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 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.…”