Hybrid quantization of an inflationary model: The flat case

We present a complete quantization of an approximately homogeneous and isotropic universe with small scalar perturbations. We consider the case in which the matter content is a minimally coupled scalar field and the spatial sections are flat and compact, with the topology of a three-torus. The quant...

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Detalles Bibliográficos
Autores: Fernández Méndez, Mikel, Mena Marugán, Guillermo A., Olmedo, Javier
Tipo de recurso: artículo
Fecha de publicación:2013
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/104019
Acceso en línea:http://hdl.handle.net/10261/104019
Access Level:acceso abierto
Palabra clave:[PACS] Quantum cosmology
[PACS] Lower dimensional models
minisuperspace models
[PACS] Loop quantum gravity, quantum geometry, spin foams
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spelling Hybrid quantization of an inflationary model: The flat caseFernández Méndez, MikelMena Marugán, Guillermo A.Olmedo, Javier[PACS] Quantum cosmology[PACS] Lower dimensional modelsminisuperspace models[PACS] Loop quantum gravity, quantum geometry, spin foamsWe present a complete quantization of an approximately homogeneous and isotropic universe with small scalar perturbations. We consider the case in which the matter content is a minimally coupled scalar field and the spatial sections are flat and compact, with the topology of a three-torus. The quantization is carried out along the lines that were put forward by the authors in a previous work for spherical topology. The action of the system is truncated at second order in perturbations. The local gauge freedom is fixed at the classical level, although different gauges are discussed and shown to lead to equivalent conclusions. Moreover, descriptions in terms of gauge-invariant quantities are considered. The reduced system is proven to admit a symplectic structure, and its dynamical evolution is dictated by a Hamiltonian constraint. Then, the background geometry is polymerically quantized, while a Fock representation is adopted for the inhomogeneities. The latter is selected by uniqueness criteria adapted from quantum field theory in curved spacetimes, which determine a specific scaling of the perturbations. In our hybrid quantization, we promote the Hamiltonian constraint to an operator on the kinematical Hilbert space. If the zero mode of the scalar field is interpreted as a relational time, a suitable ansatz for the dependence of the physical states on the polymeric degrees of freedom leads to a quantum wave equation for the evolution of the perturbations. Alternatively, the solutions to the quantum constraint can be characterized by their initial data on the minimum-volume section of each superselection sector. The physical implications of this model will be addressed in a future work, in order to check whether they are compatible with observations. © 2013 American Physical Society. This work was supported by Project No. MICINN/MINECO FIS2011- 30145-C03-02 from Spain. M. F.-M. acknowledges CSIC and the European Social Fund for support under Grant No. JAEPre_2010_01544.Peer ReviewedAmerican Physical Society2014201420132014info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501http://hdl.handle.net/10261/104019reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Inglésinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/1040192026-05-22T06:33:51Z
dc.title.none.fl_str_mv Hybrid quantization of an inflationary model: The flat case
title Hybrid quantization of an inflationary model: The flat case
spellingShingle Hybrid quantization of an inflationary model: The flat case
Fernández Méndez, Mikel
[PACS] Quantum cosmology
[PACS] Lower dimensional models
minisuperspace models
[PACS] Loop quantum gravity, quantum geometry, spin foams
title_short Hybrid quantization of an inflationary model: The flat case
title_full Hybrid quantization of an inflationary model: The flat case
title_fullStr Hybrid quantization of an inflationary model: The flat case
title_full_unstemmed Hybrid quantization of an inflationary model: The flat case
title_sort Hybrid quantization of an inflationary model: The flat case
dc.creator.none.fl_str_mv Fernández Méndez, Mikel
Mena Marugán, Guillermo A.
Olmedo, Javier
author Fernández Méndez, Mikel
author_facet Fernández Méndez, Mikel
Mena Marugán, Guillermo A.
Olmedo, Javier
author_role author
author2 Mena Marugán, Guillermo A.
Olmedo, Javier
author2_role author
author
dc.subject.none.fl_str_mv [PACS] Quantum cosmology
[PACS] Lower dimensional models
minisuperspace models
[PACS] Loop quantum gravity, quantum geometry, spin foams
topic [PACS] Quantum cosmology
[PACS] Lower dimensional models
minisuperspace models
[PACS] Loop quantum gravity, quantum geometry, spin foams
description We present a complete quantization of an approximately homogeneous and isotropic universe with small scalar perturbations. We consider the case in which the matter content is a minimally coupled scalar field and the spatial sections are flat and compact, with the topology of a three-torus. The quantization is carried out along the lines that were put forward by the authors in a previous work for spherical topology. The action of the system is truncated at second order in perturbations. The local gauge freedom is fixed at the classical level, although different gauges are discussed and shown to lead to equivalent conclusions. Moreover, descriptions in terms of gauge-invariant quantities are considered. The reduced system is proven to admit a symplectic structure, and its dynamical evolution is dictated by a Hamiltonian constraint. Then, the background geometry is polymerically quantized, while a Fock representation is adopted for the inhomogeneities. The latter is selected by uniqueness criteria adapted from quantum field theory in curved spacetimes, which determine a specific scaling of the perturbations. In our hybrid quantization, we promote the Hamiltonian constraint to an operator on the kinematical Hilbert space. If the zero mode of the scalar field is interpreted as a relational time, a suitable ansatz for the dependence of the physical states on the polymeric degrees of freedom leads to a quantum wave equation for the evolution of the perturbations. Alternatively, the solutions to the quantum constraint can be characterized by their initial data on the minimum-volume section of each superselection sector. The physical implications of this model will be addressed in a future work, in order to check whether they are compatible with observations. © 2013 American Physical Society.
publishDate 2013
dc.date.none.fl_str_mv 2013
2014
2014
2014
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/104019
url http://hdl.handle.net/10261/104019
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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