  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.
