Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2007-12-11
Comm.Math.Phys.285:1129-1163,2009; Commun.Math.Phys.285:1129-1163,2009
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
32 pages, 1 figure, to appear on Comm. Math. Phys., dedicated to Professor Klaus Fredenhagen on the occasion of his 60th birth
Scientific paper
10.1007/s00220-008-0653-8
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 $\scrim$ 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 $\lambda$ on $\cW(\scrim)$ which fulfils a suitable energy-positivity condition with respect to a generator related with the cosmological time displacements. Furthermore $\lambda$ induces a preferred physically meaningful quantum state $\lambda_M$ 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 $\lambda_M$ has positive spectrum (i.e. energy). Moreover $\lambda_M$ 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, $\lambda_M$ coincides with the Euclidean (Bunch-Davies) vacuum state, hence being Hadamard in this case. Remarks on the validity of the Hadamard property for $\lambda_M$ in more general spacetimes are presented.
Dappiaggi Claudio
Moretti Valter
Pinamonti Nicola
No associations
LandOfFree
Cosmological horizons and reconstruction of quantum field theories does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Cosmological horizons and reconstruction of quantum field theories, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cosmological horizons and reconstruction of quantum field theories will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-474570