Coarse-Grained Effective Action and Renormalization Group Theory in Semiclassical Gravity and Cosmology

TL;DR

This paper introduces techniques for analyzing quantum processes in dynamical spacetimes using effective actions and renormalization group theory, with applications to inflation, cosmology, and stochastic gravity.

Contribution

It develops a comprehensive framework combining coarse-grained effective actions and RG methods for nonequilibrium quantum processes in cosmology.

Findings

Treats eternal inflation as static critical phenomena

Derives RG equations for semiclassical gravity

Formulates Einstein-Langevin equation in stochastic gravity

Abstract

In this report we introduce the basic techniques (of the Closed Time Path - Coarse Grained Effective Action CTP-CGEA) and ideas (scaling, coarse-graining and backreaction) behind the treatment of quantum processes in dynamical background spacetimes and fields. We show how they are useful for the construction of renormalization group (RG) theories for studying these nonequilibrium processes and discuss the underlying issues. Examples are drawn from quantum field processes in an inflationary universe, semiclassical cosmology and stochastic gravity. In Part I we show how eternal inflation can be treated as static critical phenomena, while a `slow-roll' or power-law inflation can be treated as dynamical critical phenomena. In Part II we introduce the key concepts in open systems and discuss the relation of coarse-graining and backreaction. In Part III we present the CTP - CGEA. We perform perturbative and nonperturbative evaluations, and show how to derive RG equations. In Part IV, we use the RG equations to derive the Einstein-Langevin equation in stochastic semiclassical gravity. We end with a discussion on why a stochastic component of RG equations is expected for nonequilibrium processes