Large Inflationary Logarithms in a Nontrivial Nonlinear Sigma Model

TL;DR

This paper investigates large inflationary logarithms in a complex nonlinear sigma model, demonstrating their persistence beyond models reducible to free theories, and computes key quantum corrections at 1-loop and 2-loop levels.

Contribution

It introduces a nonlinear sigma model that cannot be simplified to free theories and analyzes the evolution of its background with quantum corrections.

Findings

Large logarithms appear in the model's quantum corrections.

Computed 1-loop beta and gamma functions for the model.

Demonstrated the persistence of large logs beyond free theory reductions.

Abstract

Loops of inflationary gravitons are known to induce large temporal and spatial logarithms which can cause perturbation theory to break down. Nonlinear sigma models possess the same kind of derivative interactions and induce the same sorts of large logarithms, without the complicated index structure and potential gauge problem. Previous studies have examined models with zero field space curvature which can be reduced to free field theories by local, invertible field redefinitions. Here we study a model which cannot be so reduced and still shows the same sorts of large logarithms. We compute the evolution of the background at 1-loop and 2-loop orders, and we find the 1-loop $\beta$ and $\gamma$ functions.