Preferred instantaneous vacuum for linear scalar fields in cosmological space-times

Abstract

We discuss the problem of defining a preferred vacuum state at a given time for a quantized scalar field in Friedmann, Lemaître, Robertson Walker (FLRW) space-time. Among the infinitely many homogeneous, isotropic vacua available in the theory, we show that there exists at most one for which every Fourier mode makes vanishing contribution to the adiabatically renormalized energy-momentum tensor at any given instant. For massive fields such a state exists in the most commonly used backgrounds in cosmology, and provides a natural candidate for the ground state at that instant of time. The extension to the massless and the conformally coupled case are also discussed.

19 pages, 4 figures. Section VI was expanded to include a discussion on semi-classical gravity. Version to appear in PRD