Cosmological horizons and reconstruction of quantum field theories

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dc.creatorDappiaggi, C.
dc.creatorMoretti, V.
dc.creatorPinamonti, N.
dc.date2007-12-11
dc.date2008-07-17
dc.date.accessioned2026-07-07T12:30:51Z
dc.date.available2026-07-07T12:30:51Z
dc.descriptionAs 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 $\scrim$ 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 $\cW(\scrim)$ constructed on the cosmological horizon. There is exactly one pure quasifree state $λ$ on $\cW(\scrim)$ which fulfils 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 $\scrim$, 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.
dc.description32 pages, 1 figure, to appear on Comm. Math. Phys., dedicated to Professor Klaus Fredenhagen on the occasion of his 60th birthday
dc.identifierhttps://arxiv.org/abs/0712.1770
dc.identifierhttp://arxiv.org/abs/0712.1770
dc.identifierComm.Math.Phys.285:1129-1163,2009; Commun.Math.Phys.285:1129-1163,2009
dc.identifierdoi:10.1007/s00220-008-0653-8
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/216261
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleCosmological horizons and reconstruction of quantum field theories
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