Phase space analysis and singularity classification for linearly interacting dark energy models
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Regular Article - Theoretical Physics
Phase space analysis and singularity classification for linearly interacting dark energy models Muhsin Aljaf1,a , Daniele Gregoris2,3,b , Martiros Khurshudyan1,4,5,c 1
Department of Astronomy and CAS Key Laboratory for Research in Galaxies and Cosmology, University of Science and Technology of China, Hefei 230026, Anhui, China 2 Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, 180 Siwangting Road, Yangzhou 225002, Jiangsu, China 3 School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, 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
Received: 1 November 2019 / Accepted: 22 January 2020 © The Author(s) 2020
Abstract 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 latetime 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.
1 Introduction Late-time interactions between dark energy and dark matter do not violate current observational constraints [1,2]. In particular, it has been proposed that energy flows between the two dark components of the Universe can alleviate the “coincidence problem”: why do we live in a special epoch a e-mail:
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of the evolution of our Universe in which the amounts of dark energy and dark matter are of the same order of magnitude? [3–5]. Furthermore, they may mitigate as well the Hubble tension [6], and they have been investigated in light of the 21-cm line excess at cosmic dawn by one of us [7]. On the other hand, the picture of the dark energy fluid as a cosmological constant term entering the Einstein equations is problematic due to many reasons: it violates the causality principle, its adiabatic speed of sound is ill-defined, th
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