Attractor States and Quantum Instabilities in de Sitter Space

Abstract

The asymptotic behavior of the energy–momentum tensor for a free quantized scalar field with mass m and curvature coupling ξ in de Sitter space is investigated. It is shown that for an arbitrary, homogeneous, and isotropic, fourth-order adiabatic state for which the two-point function is infrared finite, 〈T _ab〉 approaches the Bunch–Davies de Sitter invariant value at late times if m ² + ξ R > 0. In the case m = ξ = 0, the energy–momentum tensor approaches the de Sitter invariant Allen–Folacci value for such a state. For m ² + ξ R = 0 but m and ξ not separately zero, it is shown that at late times 〈T _ab〉 grows linearly in terms of cosmic time leading to an instability of de Sitter space. The asymptotic behavior is again independent of the state of the field. For m ² + ξ R < 0, it is shown that, for most values of m and ξ, 〈T _ab〉 grows exponentially in terms of cosmic time at late times in a state dependent manner.