Regular Article - Theoretical Physics
Phase space analysis and singularity classification for linearly interacting dark energy models
Department of Astronomy and CAS Key Laboratory for Research in Galaxies and Cosmology, University of Science and Technology of China, 230026, Hefei, Anhui, China
2 Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, 180 Siwangting Road, 225002, Yangzhou, Jiangsu, China
3 School of Aeronautics and Astronautics, Shanghai Jiao Tong University, 200240, Shanghai, China
4 Institut de Ciencies de lEspai (ICE-CSIC), Campus UAB, Carrer de Can Magrans, s/n, Cerdanyola del Valles, 08193, Barcelona, Spain
5 International Laboratory for Theoretical Cosmology, Tomsk State University of Control Systems and Radioelectronics (TUSUR), 634050, Tomsk, Russia
Accepted: 22 January 2020
Published online: 11 February 2020
In this paper, applying the Hartman–Grobman theorem we carry out a qualitative late-time analysis of some unified dark energy-matter Friedmann cosmological models, where the two interact through linear energy exchanges, and the dark energy fluid obeys to the dynamical equation of state of Redlich–Kwong, Modified Berthelot, and Dieterici respectively. The identification of appropriate late-time attractors allows to restrict the range of validity of the free parameters of the models under investigation. In particular, we prove that the late-time attractors which support a negative deceleration parameter correspond to a de Sitter universe. We show that the strength of deviation from an ideal fluid for the dark energy does not influence the stability of the late-time attractors, as well as the values of all the cosmological parameters at equilibrium, but for the Hubble function (which represents the age of the universe). Our analysis also shows that a singularity in the effective equation of state parameter for the dark energy fluid is not possible within this class of models.
© The Author(s) 2020
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3