The Infrared Stability of de Sitter Quantum Field Theory

In this thesis we investigate the infrared behavior of interacting massive scalar field theories on de Sitter space. We consider theories with arbitrary polynomial couplings in general spacetime dimension, and we include scalars in both the complementary and principal series of the de Sitter group SO(D, 1). We focus our attention on the Hartle-Hawking state. This state is defined by the analytic continuation of the vacuum correlation functions computed on the Euclidean section of de Sitter. Our primary result is to show that in any theory of interacting massive scalars the Hartle-Hawking state is perturbatively well-defined and stable in the infrared. We prove this result to all orders in perturbation theory. In particular, we show that the connected correlation functions of the Hartle-Hawking state decay when evaluated at large timelike separations. As a result, the Hartle-Hawking correlation functions satisfy timelike clustering, a version of cluster decomposition associated with timelike distances. We provide explicit examples in a number of theories. We also investigate the relation between our Euclidean techniques and manifestly Lorentz-signature perturbation theory. We give an analytic argument that the Hartle-Hawking state is equivalent to the vacuum state defined by in-in perturbation theory in the Poincare patch of de Sitter. We support this argument via direct calculation in simple examples. Throughout our analysis, we are careful to properly treat the ultraviolet divergences that arise in perturbation theory. Finally, we study a scenario recently considered by Krotov and Polyakov in which the coupling g turns on smoothly at finite time, starting from g = 0 in the far past where the state is taken to be the (free) Bunch-Davies vacuum. We find that the resulting correlation functions (which we compute explicitly in Lorentz-signature, and at the 1-loop level) approach those of the interacting Hartle-Hawking state at late times. We argue that similar results should hold for other physically-motivated choices of initial conditions. This result indicates that physically motivated initial conditions result in states that are well-described by excitations of the Hartle-Hawking state and thus stable in the infrared.