Cosmological Horizons and Reconstruction of Quantum Field Theories |
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Authors: | Claudio Dappiaggi Valter Moretti and Nicola Pinamonti |
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Institution: | 1.II. Institut für Theoretische Physik,Universit?t Hamburg,Hamburg,Germany;2.Istituto Nazionale di Fisica Nucleare-Gruppo Collegato,Trento,Italy;3.Dipartimento di Matematica,Università di Trento,Povo,Italy;4.Istituto Nazionale di Alta Matematica “F.Severi”– GNFM,Sesto Fiorentino,Italy |
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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 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 constructed on the cosmological horizon. There is exactly one pure quasifree state λ on 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 , 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.
Dedicated to Professor Klaus Fredenhagen on the occasion of his 60th birthday. |
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