A preferred ground state for the scalar field in de Sitter space

Aslanbeigi, Siavash; Buck, Michel

doi:10.1007/jhep08(2013)039

Cited by 13 publications

(65 citation statements)

References 49 publications

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“…A fundamental result of this paper is the explicit expression of the solutions established in part 5, that shows the dynamics of the fields is mainly governed by that of the scalar fields in dS 3 : the waves propagating on the Witten space-time are represented by a Kaluza-Klein tower, i.e. a sum of waves on dS 3 . We perform the complete spectral analysis of the self-adjoint operator L. If Φ(λ, .)…”

Section: E(u T) =| ∂ T U(t) |mentioning

confidence: 97%

“…We shall see that ρ = R does not locate a boundary, but a surface of minimal area, the bubble of nothing, that is just the 3-dimensional De Sitter space-time dS 3 : ds…”

Section: The Witten Space-timementioning

confidence: 98%

“…Therefore M is foliated by the two-parameter family of submanifolds defined by x = Cst., ψ = Cst., of De Sitter spacetimes dS 3 . In this section, we establish several analytic expressions of the scalar field as a superposition of Klein-Gordon waves on the 2+1-dimensional De Sitter spacetime…”

Section: Spectral Representationsmentioning

confidence: 99%

“…that is just the Klein-Gordon equation with mass √ λ = √ λ k on the De Sitter space-time dS 3 , and the energy of u is the sum of the energies of u k : (V.11)…”

Section: Spectral Representationsmentioning

confidence: 99%

“…In particular the set B = {| ξ ξ ξ | 2 −τ 2 = R 2 } is not a boundary but a surface of minimal area isometric with the 2+1-dimensional de Sitter space dS 3 …”

Section: Introductionmentioning

confidence: 99%

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Waves in the Witten Bubble of Nothing and the Hawking Wormhole

Bachelot

2016

Commun. Math. Phys.

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Abstract. We investigate the propagation of the scalar waves in the Witten space-time called "bubble of nothing" and in its remarkable sub-manifold, the Lorentzian Hawking wormhole. Due to the global hyperbolicity, the global Cauchy problem is well-posed in the functional framework associated with the energy. We perform a complete spectral analysis that allows to get an explicit form of the solutions in terms of special functions. If the effective mass is non zero, the profile of the waves is asymptotically almost periodic in time. In contrast, the massless case is dispersive. We develop the scattering theory, classical as well as quantum. The quantized scattering operator leaves invariant the Fock vacuum: there is no creation of particles. The resonances can be defined in the massless case and they are purely imaginary.

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Section: E(u T) =| ∂ T U(t) |mentioning

confidence: 97%

“…We shall see that ρ = R does not locate a boundary, but a surface of minimal area, the bubble of nothing, that is just the 3-dimensional De Sitter space-time dS 3 : ds…”

Section: The Witten Space-timementioning

confidence: 98%

Section: Spectral Representationsmentioning

confidence: 99%

“…that is just the Klein-Gordon equation with mass √ λ = √ λ k on the De Sitter space-time dS 3 , and the energy of u is the sum of the energies of u k : (V.11)…”

Section: Spectral Representationsmentioning

confidence: 99%

“…In particular the set B = {| ξ ξ ξ | 2 −τ 2 = R 2 } is not a boundary but a surface of minimal area isometric with the 2+1-dimensional de Sitter space dS 3 …”

Section: Introductionmentioning

confidence: 99%

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