De Sitter Wavefunctionals and the Resummation of Time

Inflationary cosmology predicts a nearly scalar-invariant spectrum of temperature fluctuation. While this is spectacularly confirmed by measurements of the Cosmic Microwave Background, it leads to conceptual complications. A massless scalar in De Sitter has infrared divergences at the level of its propagator, which has strictly scale-invariant dependence, 1/k^3. The framework of stochastic inflation uses nonperturbative insight to tame bad behavior in the perturbation series of a massless scalar in DS at late times. Remarkably, this fully quantum system loses phase information and exhibits semiclassical dynamics in the leading approximation. From simple scaling arguments, one can isolate the dominant contribution to any correlation function. We derive stochastic inflation via a novel diagrammatic method to all orders in perturbation theory. The semi-classicality of modes outside the horizon emerges at the Feynman diagram level. The wavefunctional approach to Quantum Field Theory allows us to extend these results to the nonperturbative regime. The apparently diverging series becomes well behaved in the nonperturbative approach, allowing us to claim a “resummation of time.” These results have implications for the holographic dual De Sitter, eternal inflation, and similar IR behavior of the graviton.