Cosmological singularity theorems for f(R) gravity theories

In the present work some generalizations of the Hawking singularity theorems in the context of f(R) theories are presented. The main assumptions are: the matter fields stress energy tensor satisfies the condition (Tij-(gij/2)T)kikj ≥ 0 for any generic unit time like field ki; the scalaron takes boun...

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Autor principal: Santillán, Osvaldo Pablo
Publicado: 2016
Materias:
cosmic singularity
modified gravity
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14757516_v2016_n5_p_Alani
http://hdl.handle.net/20.500.12110/paper_14757516_v2016_n5_p_Alani
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_14757516_v2016_n5_p_Alani
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spelling paper:paper_14757516_v2016_n5_p_Alani2023-06-08T16:17:57Z Cosmological singularity theorems for f(R) gravity theories Santillán, Osvaldo Pablo cosmic singularity modified gravity In the present work some generalizations of the Hawking singularity theorems in the context of f(R) theories are presented. The main assumptions are: the matter fields stress energy tensor satisfies the condition (Tij-(gij/2)T)kikj ≥ 0 for any generic unit time like field ki; the scalaron takes bounded positive values during its evolution and the resulting space time is globally hyperbolic. Then, if there exist a Cauchy hyper-surface Σ for which the expansion parameter θ of the geodesic congruence emanating orthogonally from Σ satisfies some specific bounds, then the resulting space time is geodesically incomplete. Some mathematical results of reference [92] are very important for proving this. The generalized theorems presented here apply directly for some specific models such as the Hu-Sawicki or Starobinsky ones [27,38]. For other scenarios, some extra assumptions should be implemented in order to have a geodesically incomplete space time. The hypothesis considered in this text are sufficient, but not necessary. In other words, their negation does not imply that a singularity is absent. © 2016 IOP Publishing Ltd and Sissa Medialab srl. Fil:Santillán, O.P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14757516_v2016_n5_p_Alani http://hdl.handle.net/20.500.12110/paper_14757516_v2016_n5_p_Alani
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic cosmic singularity
modified gravity
spellingShingle cosmic singularity
modified gravity
Santillán, Osvaldo Pablo
Cosmological singularity theorems for f(R) gravity theories
topic_facet cosmic singularity
modified gravity
description In the present work some generalizations of the Hawking singularity theorems in the context of f(R) theories are presented. The main assumptions are: the matter fields stress energy tensor satisfies the condition (Tij-(gij/2)T)kikj ≥ 0 for any generic unit time like field ki; the scalaron takes bounded positive values during its evolution and the resulting space time is globally hyperbolic. Then, if there exist a Cauchy hyper-surface Σ for which the expansion parameter θ of the geodesic congruence emanating orthogonally from Σ satisfies some specific bounds, then the resulting space time is geodesically incomplete. Some mathematical results of reference [92] are very important for proving this. The generalized theorems presented here apply directly for some specific models such as the Hu-Sawicki or Starobinsky ones [27,38]. For other scenarios, some extra assumptions should be implemented in order to have a geodesically incomplete space time. The hypothesis considered in this text are sufficient, but not necessary. In other words, their negation does not imply that a singularity is absent. © 2016 IOP Publishing Ltd and Sissa Medialab srl.
author Santillán, Osvaldo Pablo
author_facet Santillán, Osvaldo Pablo
author_sort Santillán, Osvaldo Pablo
title Cosmological singularity theorems for f(R) gravity theories
title_short Cosmological singularity theorems for f(R) gravity theories
title_full Cosmological singularity theorems for f(R) gravity theories
title_fullStr Cosmological singularity theorems for f(R) gravity theories
title_full_unstemmed Cosmological singularity theorems for f(R) gravity theories
title_sort cosmological singularity theorems for f(r) gravity theories
publishDate 2016
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14757516_v2016_n5_p_Alani
http://hdl.handle.net/20.500.12110/paper_14757516_v2016_n5_p_Alani
work_keys_str_mv AT santillanosvaldopablo cosmologicalsingularitytheoremsforfrgravitytheories
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