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

December 21, 2008

In a recent paper, we proved that a large class of spacetimes, not
necessarily homogeneous or isotropous and relevant at a cosmological level,
possesses a preferred codimension one submanifold, i.e., the past cosmological
horizon, on which it is possible to encode the information of a scalar field
theory living in the bulk. Such bulk-to-boundary reconstruction procedure
entails the identification of a preferred quasifree algebraic state for the
bulk theory, enjoying remarkable properties concerning invariance under
isometries (if any) of the bulk and energy positivity, and reducing to
well-known vacua in standard situations. In this paper, specialising to open
FRW models, we extend previously obtained results and we prove that the
preferred state is of Hadamard form, hence the backreaction on the metric is
finite and the state can be used as a starting point for renormalisation
procedures. That state could play a distinguished role in the discussion of the
evolution of scalar fluctuations of the metric, an analysis often performed in
the development of any model describing the dynamic of an early Universe which
undergoes an inflationary phase of rapid expansion in the past.

Keywords:

QFT on curved spacetimes, Hadamard states, cosmological spacetimes