ATTRACTOR STATES AND QUANTUM INSTABILITIES IN DE SITTER SPACE

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, 〈Tab〉 approaches the Bunch–Davies de Sitter invariant value at late times if m2 + 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 m2 + ξ R = 0 but m and ξ not separately zero, it is shown that at late times 〈Tab〉 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 m2 + ξ R < 0, it is shown that, for most values of m and ξ, 〈Tab〉 grows exponentially in terms of cosmic time at late times in a state dependent manner.