Stress-Energy Tensor Fluctuations in de Sitter Space

Abstract

The main goal of this chapter is the calculation of the noise kernel in de Sitter spacetime, in a de Sitter-invariant vacuum. The geometry of most inflationary models is well approximated by the de Sitter geometry. For this reason, fluctuations around de Sitter and near-de Sitter spacetimes have been extensively studied in the context of inflationary models. Here we study the stress-energy tensor fluctuations of the matter fields described by the noise kernel. We start by reviewing the basic geometric properties of de Sitter spacetime and the invariant bitensors that will be used in this and in later chapters. These tools are employed to write the noise kernel for spacelike separated points in de Sitter-invariant form, and explicit expressions for the case of a free minimally coupled scalar field are derived. Closed results in terms of elementary functions are given for the particular cases of small masses, vanishing mass and large separations. A massless limit discontinuity is found, and is analyzed in some detail. Finally, we discuss the implications of our results for the quantum metric fluctuations around de Sitter spacetime.