Gauge-invariant perturbations in hybrid quantum cosmology

We consider cosmological perturbations around homogeneous and isotropic spacetimes minimally coupled to a scalar field and present a formulation which is designed to preserve covariance. We truncate the action at quadratic perturbative order and particularize our analysis to flat compact spatial sec...

Descripción completa

Detalles Bibliográficos
Autores: Castelló Gomar, Laura, Martín Benito, Mercedes, Mena Marugán, Guillermo Antonio
Tipo de recurso: artículo
Fecha de publicación:2015
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/98768.2
Acceso en línea:https://hdl.handle.net/20.500.14352/98768.2
Access Level:acceso abierto
Palabra clave:530.145
Cosmological perturbation theory
Quantum cosmology
Teoría de los quanta
2212 Física Teórica
id ES_3ed61883e016c1c55b2fb8d5cb85b708
oai_identifier_str oai:docta.ucm.es:20.500.14352/98768.2
network_acronym_str ES
network_name_str España
repository_id_str
spelling Gauge-invariant perturbations in hybrid quantum cosmologyCastelló Gomar, LauraMartín Benito, MercedesMena Marugán, Guillermo Antonio530.145Cosmological perturbation theoryQuantum cosmologyTeoría de los quanta2212 Física TeóricaWe consider cosmological perturbations around homogeneous and isotropic spacetimes minimally coupled to a scalar field and present a formulation which is designed to preserve covariance. We truncate the action at quadratic perturbative order and particularize our analysis to flat compact spatial sections and a field potential given by a mass term, although the formalism can be extended to other topologies and potentials. The perturbations are described in terms of Mukhanov-Sasaki gauge invariants, linear perturbative constraints, and variables canonically conjugate to them. This set is completed into a canonical one for the entire system, including the homogeneous degrees of freedom. We find the global Hamiltonian constraint of the model, in which the contribution of the homogeneous sector is corrected with a term quadratic in the perturbations, that can be identified as the Mukhanov-Sasaki Hamiltonian in our formulation. We then adopt a hybrid approach to quantize the model, combining a quantum representation of the homogeneous sector with a more standard field quantization of the perturbations. Covariance is guaranteed in this approach inasmuch as no gauge fixing is adopted. Next, we adopt a Born-Oppenheimer ansatz for physical states and show how to obtain a Schrödinger-like equation for the quantum evolution of the perturbations. This evolution is governed by the Mukhanov-Sasaki Hamiltonian, with the dependence on the homogeneous geometry evaluated at quantum expectation values, and with a time parameter defined also in terms of suitable expectation values on that geometry. Finally, we derive effective equations for the dynamics of the Mukhanov-Sasaki gauge invariants, that include quantum contributions, but have the same ultraviolet limit as the classical equations. They provide the master equation to extract predictions about the power spectrum of primordial scalar perturbations.IOP PublishingUniversidad Complutense de Madrid20152015-06-2620152015-06-26journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/98768.2reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)InglésengMinisterio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 FIS2011-30145-C03-02 Not availableMinisterio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 FIS2014-54800-C2-2-P Not available62001772 Not available Not availableopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/98768.22026-06-02T12:44:21Z
dc.title.none.fl_str_mv Gauge-invariant perturbations in hybrid quantum cosmology
title Gauge-invariant perturbations in hybrid quantum cosmology
spellingShingle Gauge-invariant perturbations in hybrid quantum cosmology
Castelló Gomar, Laura
530.145
Cosmological perturbation theory
Quantum cosmology
Teoría de los quanta
2212 Física Teórica
title_short Gauge-invariant perturbations in hybrid quantum cosmology
title_full Gauge-invariant perturbations in hybrid quantum cosmology
title_fullStr Gauge-invariant perturbations in hybrid quantum cosmology
title_full_unstemmed Gauge-invariant perturbations in hybrid quantum cosmology
title_sort Gauge-invariant perturbations in hybrid quantum cosmology
dc.creator.none.fl_str_mv Castelló Gomar, Laura
Martín Benito, Mercedes
Mena Marugán, Guillermo Antonio
author Castelló Gomar, Laura
author_facet Castelló Gomar, Laura
Martín Benito, Mercedes
Mena Marugán, Guillermo Antonio
author_role author
author2 Martín Benito, Mercedes
Mena Marugán, Guillermo Antonio
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 530.145
Cosmological perturbation theory
Quantum cosmology
Teoría de los quanta
2212 Física Teórica
topic 530.145
Cosmological perturbation theory
Quantum cosmology
Teoría de los quanta
2212 Física Teórica
description We consider cosmological perturbations around homogeneous and isotropic spacetimes minimally coupled to a scalar field and present a formulation which is designed to preserve covariance. We truncate the action at quadratic perturbative order and particularize our analysis to flat compact spatial sections and a field potential given by a mass term, although the formalism can be extended to other topologies and potentials. The perturbations are described in terms of Mukhanov-Sasaki gauge invariants, linear perturbative constraints, and variables canonically conjugate to them. This set is completed into a canonical one for the entire system, including the homogeneous degrees of freedom. We find the global Hamiltonian constraint of the model, in which the contribution of the homogeneous sector is corrected with a term quadratic in the perturbations, that can be identified as the Mukhanov-Sasaki Hamiltonian in our formulation. We then adopt a hybrid approach to quantize the model, combining a quantum representation of the homogeneous sector with a more standard field quantization of the perturbations. Covariance is guaranteed in this approach inasmuch as no gauge fixing is adopted. Next, we adopt a Born-Oppenheimer ansatz for physical states and show how to obtain a Schrödinger-like equation for the quantum evolution of the perturbations. This evolution is governed by the Mukhanov-Sasaki Hamiltonian, with the dependence on the homogeneous geometry evaluated at quantum expectation values, and with a time parameter defined also in terms of suitable expectation values on that geometry. Finally, we derive effective equations for the dynamics of the Mukhanov-Sasaki gauge invariants, that include quantum contributions, but have the same ultraviolet limit as the classical equations. They provide the master equation to extract predictions about the power spectrum of primordial scalar perturbations.
publishDate 2015
dc.date.none.fl_str_mv 2015
2015-06-26
2015
2015-06-26
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/98768.2
url https://hdl.handle.net/20.500.14352/98768.2
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 FIS2011-30145-C03-02 Not available
Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 FIS2014-54800-C2-2-P Not available
62001772 Not available Not available
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv IOP Publishing
publisher.none.fl_str_mv IOP Publishing
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869406586153205760
score 15,81155

Similares en LA Referencia