Cosmological horizons and reconstruction of quantum field theories

As a starting point for this manuscript, we remark how the cosmological horizon of a certain class of Friedmann-Robertson-Walker backgrounds shares some non trivial geometric properties with infinity in an asymptotically flat spacetime. Such a feature is generalized to a larger class of expanding spacetimes M admitting a geodesically complete cosmological horizon $\Im^-$ common to all co-moving observers. This property 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 infinity. Under suitable hypotheses on M the algebra of observables for a Klein-Gordon field in M is mapped into a subalgebra of the algebra of observables W($\Im^-$) constructed on the cosmological horizon. There is exactly one pure quasifree state λ on W($\Im^-$) which fulfills a suitable energy-positivity condition with respect to a generator related with the cosmological time translations. Furthermore λ induces a preferred physically meaningful quantum state λM for the quantum theory in M. If M admits a timelike Killing generator preserving $\Im^-$, then the associated self-adjoint generator in the GNS representation of λM has positive spectrum (i.e. energy). λM turns out to be invariant under every symmetry of M which preserve the cosmological horizon. In the case of an expanding de Sitter spacetime, λM coincides with the Euclidean (Bunch-Davies) vacuum state, hence being Hadamard in this case.