Summing Inflationary Logarithms in Nonlinear Sigma Models

TL;DR

This paper investigates how large logarithmic corrections in nonlinear sigma models on de Sitter space can be summed using stochastic and renormalization group techniques, revealing insights into quantum effects in curved spacetime.

Contribution

It introduces methods to sum inflationary logarithms in nonlinear sigma models, extending stochastic formalism and renormalization group approaches to curved backgrounds.

Findings

Large logarithms cause perturbation theory breakdown at late times and large distances.

Starobinsky's stochastic formalism can sum tail-related logarithms.

Renormalization group methods can sum ultraviolet-related logarithms.

Abstract

We consider two nonlinear sigma models on de Sitter background which involve the same derivative interactions as quantum gravity but without the gauge issue. The first model contains only a single field, which can be reduced to a free theory by a local field redefinition; the second contains two fields and cannot be so reduced. Loop corrections in both models produce large temporal and spatial logarithms which cause perturbation theory to break down at late times and large distances. Many of these logarithms derive from the "tail" part of the propagator and can be summed using a variant of Starobinsky's stochastic formalism involving a curvature-dependent effective potential. The remaining logarithms derive from the ultraviolet and can be summed using a variant of the renormalization group based on a special class of curvature-dependent renormalizations. Explicit results are derived at 1-loop and 2-loop orders.