Non-integrability of the axisymmetric Bianchi IX cosmological model via Differential Galois Theory

Fuente: arXiv
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Autori principali: Acosta-Humánez, Primitivo, Morales-Ruiz, Juan J., Stuchi, Teresinha J.
Natura: Preprint
Pubblicazione: 2021
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author Acosta-Humánez, Primitivo
Morales-Ruiz, Juan J.
Stuchi, Teresinha J.
author_facet Acosta-Humánez, Primitivo
Morales-Ruiz, Juan J.
Stuchi, Teresinha J.
contents We investigate the integrability of an anisotropic universe with matter and cosmological constant formulated as Bianchi IX models. The presence of the cosmological constant causes the existence of a critical point in the finite part of the phase space. The separatrix associated to this Einstein's static universe is entirely contained in an invariant isotropic plane forgetting the singularity at the origin. This invariant plane of isotropy is an integrable sub-space of the Taub type. In this paper we analyse the differential Galois group of the second order variational equations to this plane in order to apply the integrability theorem of the second author with Ramis and Sim\' o. The main result is that the model is non-integrable by meromorphic functions.
format Preprint
id arxiv_https___arxiv_org_abs_2102_10108
institution arXiv
publishDate 2021
record_format arxiv
spellingShingle Non-integrability of the axisymmetric Bianchi IX cosmological model via Differential Galois Theory
Acosta-Humánez, Primitivo
Morales-Ruiz, Juan J.
Stuchi, Teresinha J.
Dynamical Systems
Mathematical Physics
34M25, 35A22, 35C05, 92D25
We investigate the integrability of an anisotropic universe with matter and cosmological constant formulated as Bianchi IX models. The presence of the cosmological constant causes the existence of a critical point in the finite part of the phase space. The separatrix associated to this Einstein's static universe is entirely contained in an invariant isotropic plane forgetting the singularity at the origin. This invariant plane of isotropy is an integrable sub-space of the Taub type. In this paper we analyse the differential Galois group of the second order variational equations to this plane in order to apply the integrability theorem of the second author with Ramis and Sim\' o. The main result is that the model is non-integrable by meromorphic functions.
title Non-integrability of the axisymmetric Bianchi IX cosmological model via Differential Galois Theory
topic Dynamical Systems
Mathematical Physics
34M25, 35A22, 35C05, 92D25
url https://arxiv.org/abs/2102.10108