What if? Exploring the multiverse through Euclidean wormholes

Mariam Bouhmadi-López,Salvador Robles-Pérez,Manuel Krämer,João Morais

doi:10.1140/epjc/s10052-017-5279-6

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.

Highlights

Humankind has, ever since history can tell, been looking for possible answers and hints to the questions: Where do we come from? Where are we heading to? Cosmology is the path to address these questions on scientific grounds
We present Euclidean wormhole solutions describing possible bridges within the multiverse
Within the framework of the third quantisation, one of the current proposals to describe the multiverse, we have shown the existence of Euclidean wormhole solutions which describe possible bridges within the multiverse

Summary

Introduction

In order to obtain the evolution a(η) of the different phases of the universe in terms of the conformal time η, defined in terms of the cosmic time t via dη/dt = a−1, we need to solve the following differential equation: da(η) = ωK (a) , dη σ. A solution for the previous equation in terms of elementary functions can be obtained for the special cases of αK = 0, which corresponds to the scenario of the creation of an expanding universe from nothing [41], and of αK = π , which corresponds to the maximum value of K for which the tunnelling effect happens. Once the value a+ is reached, the universe exits the Euclidean wormhole and enters a near de Sitter expansion (depicted in green) In this final phase the scale factor grows in an accelerated fashion as the time displacement η := (η − η+)/|η(a=+∞) − η+| varies from 0 to 1

Tunnelling

Conclusions

Direct derivation

Cross-check of the integral by differentiation