General aspects of Gauss-Bonnet models without potential in dimension four

In the present work, the isotropic and homogenous solutions with spatial curvature k=0 of four dimensional Gauss-Bonnet models are characterized. The main assumption is that the scalar field φ which is coupled to the Gauss-Bonnet term has no potential [1]-[2]. Some singular and some eternal solution...

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Detalles Bibliográficos
Publicado: 2017
Materias:
cosmic singularity
modified gravity
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14757516_v2017_n7_p_Santillan
http://hdl.handle.net/20.500.12110/paper_14757516_v2017_n7_p_Santillan
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_14757516_v2017_n7_p_Santillan
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spelling paper:paper_14757516_v2017_n7_p_Santillan2023-06-08T16:17:58Z General aspects of Gauss-Bonnet models without potential in dimension four cosmic singularity modified gravity In the present work, the isotropic and homogenous solutions with spatial curvature k=0 of four dimensional Gauss-Bonnet models are characterized. The main assumption is that the scalar field φ which is coupled to the Gauss-Bonnet term has no potential [1]-[2]. Some singular and some eternal solutions are described. The evolution of the universe is given in terms of a curve γ=(H(φ), φ) which is the solution of a polynomial equation P(H2, φ)=0 with φ dependent coefficients. In addition, it is shown that the initial conditions in these models put several restrictions on the evolution. For instance, an universe initially contracting will be contracting always for future times and an universe that is expanding was always expanding at past times. Thus, there are no cyclic cosmological solutions for this model. These results are universal, that is, independent on the form of the coupling f(φ) between the scalar field and the Gauss-Bonnet term. In addition, a proof that at a turning point 0 a singularity necessarily emerges is presented, except for some specific choices of the coupling. This is valid unless the Hubble constant H 0 at this point. This proof is based on the Raychaudhuri equation for the model. The description presented here is in part inspired in the works [3]-[4]. However, the mathematical methods that are implemented are complementary of those in these references, and they may be helpful for study more complicated situations in a future. © 2017 IOP Publishing Ltd and Sissa Medialab. 2017 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14757516_v2017_n7_p_Santillan http://hdl.handle.net/20.500.12110/paper_14757516_v2017_n7_p_Santillan
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
General aspects of Gauss-Bonnet models without potential in dimension four
topic_facet cosmic singularity
modified gravity
description In the present work, the isotropic and homogenous solutions with spatial curvature k=0 of four dimensional Gauss-Bonnet models are characterized. The main assumption is that the scalar field φ which is coupled to the Gauss-Bonnet term has no potential [1]-[2]. Some singular and some eternal solutions are described. The evolution of the universe is given in terms of a curve γ=(H(φ), φ) which is the solution of a polynomial equation P(H2, φ)=0 with φ dependent coefficients. In addition, it is shown that the initial conditions in these models put several restrictions on the evolution. For instance, an universe initially contracting will be contracting always for future times and an universe that is expanding was always expanding at past times. Thus, there are no cyclic cosmological solutions for this model. These results are universal, that is, independent on the form of the coupling f(φ) between the scalar field and the Gauss-Bonnet term. In addition, a proof that at a turning point 0 a singularity necessarily emerges is presented, except for some specific choices of the coupling. This is valid unless the Hubble constant H 0 at this point. This proof is based on the Raychaudhuri equation for the model. The description presented here is in part inspired in the works [3]-[4]. However, the mathematical methods that are implemented are complementary of those in these references, and they may be helpful for study more complicated situations in a future. © 2017 IOP Publishing Ltd and Sissa Medialab.
title General aspects of Gauss-Bonnet models without potential in dimension four
title_short General aspects of Gauss-Bonnet models without potential in dimension four
title_full General aspects of Gauss-Bonnet models without potential in dimension four
title_fullStr General aspects of Gauss-Bonnet models without potential in dimension four
title_full_unstemmed General aspects of Gauss-Bonnet models without potential in dimension four
title_sort general aspects of gauss-bonnet models without potential in dimension four
publishDate 2017
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14757516_v2017_n7_p_Santillan
http://hdl.handle.net/20.500.12110/paper_14757516_v2017_n7_p_Santillan
_version_ 1768544518103105536

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