Cartan symmetries and global dynamical systems analysis in a higher-order modified teleparallel theory |
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| Authors: | L. Karpathopoulos S. Basilakos G. Leon A. Paliathanasis M. Tsamparlis |
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| Affiliation: | 1.Department of Astronomy-Astrophysics-Mechanics, Faculty of Physics,University of Athens,Athens,Greece;2.Research Center for Astronomy and Applied Mathematics,Academy of Athens,Athens,Greece;3.Departamento de Matemáticas,Universidad Católica del Norte,Antofagasta,Chile;4.Instituto de Ciencias Físicas y Matemáticas,Universidad Austral de Chile,Valdivia,Chile;5.Department of Mathematics and Natural Sciences, Core Curriculum Program,Prince Mohammad Bin Fahd University,Al Khobar,Kingdom of Saudi Arabia;6.Institute of Systems Science,Durban University of Technology,Durban,South Africa |
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| Abstract: | In a higher-order modified teleparallel theory cosmological we present analytical cosmological solutions. In particular we determine forms of the unknown potential which drives the scalar field such that the field equations form a Liouville integrable system. For the determination of the conservation laws we apply the Cartan symmetries. Furthermore, inspired from our solutions, a toy model is studied and it is shown that it can describe the Supernova data, while at the same time introduces dark matter components in the Hubble function. When the extra matter source is a stiff fluid then we show how analytical solutions for Bianchi I universes can be constructed from our analysis. Finally, we perform a global dynamical analysis of the field equations by using variables different from that of the Hubble-normalization. |
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