Coarse-grained effective action and renormalization group theory in semiclassical gravity and cosmology

In this report we introduce the basic techniques (of the closed-time-path (CTP) coarse-grained effective action (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 c...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Calzetta, E.A., Hu, B.L., Mazzitelli, F.D.
Formato:	JOUR
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_03701573_v352_n4-6_p459_Calzetta
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_03701573_v352_n4-6_p459_Calzetta
record_format	dspace
spelling	todo:paper_03701573_v352_n4-6_p459_Calzetta2023-10-03T15:28:30Z Coarse-grained effective action and renormalization group theory in semiclassical gravity and cosmology Calzetta, E.A. Hu, B.L. Mazzitelli, F.D. In this report we introduce the basic techniques (of the closed-time-path (CTP) coarse-grained effective action (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 (Sections 2, 3) we begin by establishing a relation between scaling and inflation, and show how eternal inflation (where the scale factor of the universe grows exponentially) 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 (Sections 4, 5) we introduce the key concepts in open systems and discuss the relation of coarse-graining and backreaction. We recount how the (in-out, or Schwinger-DeWitt) CGEA devised by Hu and Zhang can be used to treat some aspects of the effects of the environment on the system. This is illustrated by the stochastic inflation model where quantum fluctuations appearing as noise backreact on the inflaton field. We show how RG techniques can be usefully applied to obtain the running of coupling constants in the inflaton field, followed by a discussion of the cosmological and theoretical implications. In Part III (Sections 6-8) we present the CTP (in-in, or Schwinger-Keldysh) CGEA introduced by Hu and Sinha. We show how to calculate perturbatively the CTP CGEA for the λΦ 4 model. We mention how it is useful for calculating the backreaction of environmental fields on the system field (e.g. light on heavy, fast on slow) or one sector of a field on another (e.g. high momentum modes on low, inhomogeneous modes on homogeneous), and problems in other areas of physics where this method can be usefully applied. This is followed by an introduction to the influence functional in the (Feynman-Vernon) formulation of quantum open systems, illustrated by the quantum Brownian motion models. We show its relation to the CTP CGEA, and indicate how to identify the noise and dissipation kernels therein. We derive the master and Langevin equations for interacting quantum fields, represented in the works of Lombardo and Mazzitelli and indicate how they can be applied to the problem of coarse-graining, decoherence and structure formation in de Sitter universe. We perform a nonperturbative evaluation of the CTP CGEA and show how to derive the renormalization group equations under an adiabatic approximation adopted for the modes by Dalvit and Mazzitelli. We assert that this approximation is incomplete as the effect of noise is suppressed. We then discuss why noise is expected in the RG equations for nonequilibrium processes. In Part IV (Sections 9, 10), following Lombardo and Mazzitelli, we use the RG equations to derive the Einstein-Langevin equation in stochastic semiclassical gravity. As an example, we calculate the quantum correction to the Newtonian potential. We end with a discussion on why a stochastic component of RG equations is expected for nonequilibrium processes. © 2001 Elsevier Science B.V. All rights reserved. Fil:Calzetta, E.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Mazzitelli, F.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03701573_v352_n4-6_p459_Calzetta
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description	In this report we introduce the basic techniques (of the closed-time-path (CTP) coarse-grained effective action (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 (Sections 2, 3) we begin by establishing a relation between scaling and inflation, and show how eternal inflation (where the scale factor of the universe grows exponentially) 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 (Sections 4, 5) we introduce the key concepts in open systems and discuss the relation of coarse-graining and backreaction. We recount how the (in-out, or Schwinger-DeWitt) CGEA devised by Hu and Zhang can be used to treat some aspects of the effects of the environment on the system. This is illustrated by the stochastic inflation model where quantum fluctuations appearing as noise backreact on the inflaton field. We show how RG techniques can be usefully applied to obtain the running of coupling constants in the inflaton field, followed by a discussion of the cosmological and theoretical implications. In Part III (Sections 6-8) we present the CTP (in-in, or Schwinger-Keldysh) CGEA introduced by Hu and Sinha. We show how to calculate perturbatively the CTP CGEA for the λΦ 4 model. We mention how it is useful for calculating the backreaction of environmental fields on the system field (e.g. light on heavy, fast on slow) or one sector of a field on another (e.g. high momentum modes on low, inhomogeneous modes on homogeneous), and problems in other areas of physics where this method can be usefully applied. This is followed by an introduction to the influence functional in the (Feynman-Vernon) formulation of quantum open systems, illustrated by the quantum Brownian motion models. We show its relation to the CTP CGEA, and indicate how to identify the noise and dissipation kernels therein. We derive the master and Langevin equations for interacting quantum fields, represented in the works of Lombardo and Mazzitelli and indicate how they can be applied to the problem of coarse-graining, decoherence and structure formation in de Sitter universe. We perform a nonperturbative evaluation of the CTP CGEA and show how to derive the renormalization group equations under an adiabatic approximation adopted for the modes by Dalvit and Mazzitelli. We assert that this approximation is incomplete as the effect of noise is suppressed. We then discuss why noise is expected in the RG equations for nonequilibrium processes. In Part IV (Sections 9, 10), following Lombardo and Mazzitelli, we use the RG equations to derive the Einstein-Langevin equation in stochastic semiclassical gravity. As an example, we calculate the quantum correction to the Newtonian potential. We end with a discussion on why a stochastic component of RG equations is expected for nonequilibrium processes. © 2001 Elsevier Science B.V. All rights reserved.
format	JOUR
author	Calzetta, E.A. Hu, B.L. Mazzitelli, F.D.
spellingShingle	Calzetta, E.A. Hu, B.L. Mazzitelli, F.D. Coarse-grained effective action and renormalization group theory in semiclassical gravity and cosmology
author_facet	Calzetta, E.A. Hu, B.L. Mazzitelli, F.D.
author_sort	Calzetta, E.A.
title	Coarse-grained effective action and renormalization group theory in semiclassical gravity and cosmology
title_short	Coarse-grained effective action and renormalization group theory in semiclassical gravity and cosmology
title_full	Coarse-grained effective action and renormalization group theory in semiclassical gravity and cosmology
title_fullStr	Coarse-grained effective action and renormalization group theory in semiclassical gravity and cosmology
title_full_unstemmed	Coarse-grained effective action and renormalization group theory in semiclassical gravity and cosmology
title_sort	coarse-grained effective action and renormalization group theory in semiclassical gravity and cosmology
url	http://hdl.handle.net/20.500.12110/paper_03701573_v352_n4-6_p459_Calzetta
work_keys_str_mv	AT calzettaea coarsegrainedeffectiveactionandrenormalizationgrouptheoryinsemiclassicalgravityandcosmology AT hubl coarsegrainedeffectiveactionandrenormalizationgrouptheoryinsemiclassicalgravityandcosmology AT mazzitellifd coarsegrainedeffectiveactionandrenormalizationgrouptheoryinsemiclassicalgravityandcosmology
_version_	1782029392520675328

Coarse-grained effective action and renormalization group theory in semiclassical gravity and cosmology

Ejemplares similares