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, 77 (10), 718

What If? Exploring the Multiverse Through Euclidean Wormholes

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What If? Exploring the Multiverse Through Euclidean Wormholes

Mariam Bouhmadi-López et al. Eur Phys J C Part Fields.

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.

Figures

Fig. 1
Fig. 1
The tunnelling potential V(a)=σ2(a4-HdS2a6)
Fig. 2
Fig. 2
The evolution of the squared scale factor as a function of the conformal Lorentzian time η and conformal Euclidean time η~. In order to be able to plot the evolution of the scale factor in a single figure including the Lorentzian and Euclidean solutions, we have rescaled the conformal time as follows: for the baby universe (red) Δη=(η-η-)/|η(a=0)-η-| with Δη[-1,0]; for the Euclidean instanton (blue) Δη~=(η~-η~+)/|η~(a=a-)-η~+| with Δη~[-1,0]; for the expanding asymptotically de Sitter universe (green) Δη=(η-η+)/|η(a+)-η+| with Δη[0,1]
Fig. 3
Fig. 3
The tunnelling probability PK(a-a+) plotted as a function of the ratios γ:=ħ2HdS2/MP2 and K/Kmax. The coloured lines, which represent the tunnelling probability for a fixed value of K/Kmax (blue) or of γ (red) are compared in Fig. 4. The tunnelling probability for the case of the creation of an expanding universe from nothing (K=0) is indicated by a dashed blue line
Fig. 4
Fig. 4
The tunnelling probability PK(a-a+) plotted as (left) a function of γ for different values of K/Kmax: (from bottom/darker to top/lighter) K/Kmax=0, K/Kmax=1/4, K/Kmax=1/2, K/Kmax=3/4 and K/Kmax=99/100; and as (right) a function of the ratio K/Kmax for different values of γ:=ħ2HdS2/MP2: (from bottom/darker to top/lighter) γ=1/8, γ=3/8, γ=5/8 and γ=7/8. The tunnelling probability for the case of the creation of an expanding universe from nothing (K=0) is indicated by a dashed blue line

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