Stochastic Quantum Gravitational Inflation

TL;DR

This paper explores extending stochastic inflation techniques to quantum gravity, addressing challenges posed by derivative interactions and constrained fields through perturbative scalar models.

Contribution

It proposes rules for formulating stochastic approaches to quantum gravity, building on scalar models with derivative interactions and constraints.

Findings

Reproduces leading infrared logarithms in inflationary quantum field theories.

Develops a stochastic formulation framework for theories with derivative interactions.

Provides perturbative rules for stochastic quantization of constrained fields.

Abstract

During inflation explicit perturbative computations of quantum field theories which contain massless, non-conformal fields exhibit secular effects that grow as powers of the logarithm of the inflationary scale factor. Starobinskii's technique of stochastic inflation not only reproduces the leading infrared logarithms at each order in perturbation theory, it can sometimes be summed to reveal what happens when inflation has proceeded so long that the large logarithms overwhelm even very small coupling constants. It is thus a cosmological analogue of what the renormalization group does for the ultraviolet logarithms of quantum field theory, and generalizing this technique to quantum gravity is a problem of great importance. There are two significant differences between gravity and the scalar models for which stochastic formulations have so far been given: derivative interactions and the presence of constrained fields. We use explicit perturbative computations in two simple scalar models to infer a set of rules for stochastically formulating theories with these features.