English

Cosmological horizons and reconstruction of quantum field theories

General Relativity and Quantum Cosmology 2009-01-19 v3 High Energy Physics - Theory Mathematical Physics math.MP

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 MM admitting a geodesically complete cosmological horizon \scrim\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 MM, 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)\cW(\scrim) constructed on the cosmological horizon. There is exactly one pure quasifree state λ\lambda on \cW(\scrim)\cW(\scrim) which fulfils a suitable energy-positivity condition with respect to a generator related with the cosmological time displacements. Furthermore λ\lambda induces a preferred physically meaningful quantum state λM\lambda_M for the quantum theory in the bulk. If MM admits a timelike Killing generator preserving \scrim\scrim, then the associated self-adjoint generator in the GNS representation of λM\lambda_M has positive spectrum (i.e. energy). Moreover λM\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, λM\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 λM\lambda_M in more general spacetimes are presented.

Keywords

Cite

@article{arxiv.0712.1770,
  title  = {Cosmological horizons and reconstruction of quantum field theories},
  author = {C. Dappiaggi and V. Moretti and N. Pinamonti},
  journal= {arXiv preprint arXiv:0712.1770},
  year   = {2009}
}

Comments

32 pages, 1 figure, to appear on Comm. Math. Phys., dedicated to Professor Klaus Fredenhagen on the occasion of his 60th birthday