Cosmological horizons and reconstruction of quantum field theories

TL;DR

This paper explores the geometric properties of cosmological horizons in expanding spacetimes and demonstrates how quantum field theories can be reconstructed on these horizons, leading to a preferred quantum state that generalizes the Bunch-Davies vacuum.

Contribution

It generalizes the horizon structure and quantum field reconstruction to a broad class of expanding spacetimes, establishing a unique preferred quantum state on the horizon.

Findings

Existence of a unique pure quasifree state on the horizon

Construction of a preferred quantum state in the bulk from the horizon state

In de Sitter space, the state coincides with the Bunch-Davies vacuum

Abstract

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.