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

TL;DR

This paper identifies a unique preferred vacuum state for scalar fields in cosmological space-times, which minimizes the energy-momentum tensor contributions at a given time, aiding in defining ground states in quantum cosmology.

Contribution

It demonstrates the existence and uniqueness of a preferred vacuum state in FLRW space-times that minimizes the energy-momentum tensor contributions at a specific time.

Findings

Existence of a unique vacuum state in cosmological backgrounds.

The preferred vacuum minimizes the energy-momentum tensor contributions.

Applicability to massive, massless, and conformally coupled scalar fields.

Abstract

We discuss the problem of defining a preferred vacuum state at a given time for a quantized scalar field in Friedmann, Lema\^itre, 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.