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Cosmological Horizons and Reconstruction of Quantum Field Theories

  • Claudio Dappiaggi
  • Valter Moretti
  • Nicola Pinamonti
Article

Abstract

As a starting point, we state some relevant geometrical properties enjoyed by the cosmological horizon of a certain class of Friedmann-Robertson-Walker backgrounds. Those properties are generalised to a larger class of expanding spacetimes M admitting a geodesically complete cosmological horizon \({{\Im^-}}\) common to all co-moving observers. This structure is later exploited in order to recast, in a cosmological background, some recent results for a linear scalar quantum field theory in spacetimes asymptotically flat at null infinity. Under suitable hypotheses on M, encompassing both the cosmological de Sitter background and a large class of other FRW spacetimes, the algebra of observables for a Klein-Gordon field is mapped into a subalgebra of the algebra of observables \({{\mathcal{W}(\Im^-)}}\) constructed on the cosmological horizon. There is exactly one pure quasifree state λ on \({{\mathcal{W}(\Im^-)}}\) which fulfills a suitable energy-positivity condition with respect to a generator related with the cosmological time displacements. Furthermore λ induces a preferred physically meaningful quantum state λ M for the quantum theory in the bulk. If M admits a timelike Killing generator preserving \({{\Im^-}}\) , then the associated self-adjoint generator in the GNS representation of λ M has positive spectrum (i.e., energy). Moreover λ M turns out to be invariant under every symmetry of the bulk metric which preserves the cosmological horizon. In the case of an expanding de Sitter spacetime, λ M coincides with the Euclidean (Bunch-Davies) vacuum state, hence being Hadamard in this case. Remarks on the validity of the Hadamard property for λ M in more general spacetimes are presented.

Keywords

Symplectic Form Cauchy Surface Cosmological Horizon Conformal Killing Vector Timelike Killing Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Claudio Dappiaggi
    • 1
  • Valter Moretti
    • 2
    • 3
    • 4
  • Nicola Pinamonti
    • 1
  1. 1.II. Institut für Theoretische PhysikUniversität HamburgHamburgGermany
  2. 2.Istituto Nazionale di Fisica Nucleare-Gruppo CollegatoTrentoItaly
  3. 3.Dipartimento di MatematicaUniversità di TrentoPovoItaly
  4. 4.Istituto Nazionale di Alta Matematica “F.Severi”– GNFMSesto FiorentinoItaly

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