Infrared resummation for derivative interactions in de Sitter space

Hiroyuki Kitamoto

doi:10.1103/physrevd.100.025020

Abstract

In de Sitter space, scale invariant fluctuations give rise to infrared logarithmic corrections to physical quantities, which eventually spoil perturbation theories. For models without derivative interactions, it has been known that the field equation reduces to a Langevin equation with white noise in the leading logarithm approximation. The stochastic equation allows us to evaluate the infrared effects nonperturbatively. We extend the resummation formula so that it is applicable to models with derivative interactions. We first consider the nonlinear sigma model and next consider a more general model which consists of a noncanonical kinetic term and a potential term. The stochastic equations derived from the infrared resummation in these models can be understood as generalizations of the standard one to curved target spaces.

Highlights

In de Sitter space, the propagator for a massless and minimally coupled scalar field has a dS symmetry breaking term
The IR effects at each loop level manifest as polynomials in the IR logarithm whose degrees increase with the loop level
The leading IR effects come from the leading IR logarithms at each loop level

Summary

INTRODUCTION

In de Sitter (dS) space, the propagator for a massless and minimally coupled scalar field has a dS symmetry breaking term. In the presence of this scalar field, physical quantities may acquire time dependences through the propagator In tribute to their origin, we call them quantum infrared (IR) effects in dS space. As a specific feature of derivative interactions, we need to take into account the contribution from the subhorizon scale in evaluating the leading IR effects This fact was found in [10,11] where the energy-momentum tensor of the nonlinear sigma model was studied. At the one-loop level, ε acquires a secular growth while η does not This result indicates that if ε and η are vanishingly small at the beginning due to the pseudo shift symmetry, the quantum mechanism leads to an inflation model with a linear potential.

FREE SCALAR FIELD THEORY

ΓðzÞ dΓðzÞ dz ð2:12Þ where y denotes the square of the physical distance:

NONLINEAR SIGMA MODEL

MORE GENERAL MODEL

CONCLUSION