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 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 λM 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 λM has
positive spectrum (i.e. energy). Moreover λM 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 coincides
with the Euclidean (Bunch-Davies) vacuum state, hence being Hadamard in this
case. Remarks on the validity of the Hadamard property for λM in more
general spacetimes are presented.Comment: 32 pages, 1 figure, to appear on Comm. Math. Phys., dedicated to
Professor Klaus Fredenhagen on the occasion of his 60th birthda