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In a recent paper, we proved that a large class of spacetimes, notnecessarily homogeneous or isotropous and relevant at a cosmological level,possesses a preferred codimension one submanifold, i.e., the past cosmologicalhorizon, on which it is possible to encode the information of a scalar fieldtheory living in the bulk. Such bulk-to-boundary reconstruction procedureentails the identification of a preferred quasifree algebraic state for thebulk theory, enjoying remarkable properties concerning invariance underisometries (if any) of the bulk and energy positivity, and reducing towell-known vacua in standard situations. In this paper, specialising to openFRW models, we extend previously obtained results and we prove that thepreferred state is of Hadamard form, hence the backreaction on the metric isfinite and the state can be used as a starting point for renormalisationprocedures. That state could play a distinguished role in the discussion of theevolution of scalar fluctuations of the metric, an analysis often performed inthe development of any model describing the dynamic of an early Universe whichundergoes an inflationary phase of rapid expansion in the past.

Distinguished quantum states in a class of cosmological spacetimes and their Hadamard property