Cosmological Horizons and Reconstruction of Quantum Field Theories

  • Claudio Dappiaggi
  • Valter MorettiEmail author
  • Nicola Pinamonti


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.


Symplectic Form Cauchy Surface Cosmological Horizon Conformal Killing Vector Timelike Killing Vector 
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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Claudio Dappiaggi
    • 1
  • Valter Moretti
    • 2
    • 3
    • 4
    Email author
  • 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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