https://doi.org/10.1140/epjc/s10052-019-6875-4
Regular Article - Theoretical Physics
Dynamical system analysis of a three fluid cosmological model: an invariant manifold approach
1
Department of Mathematics, Sister Nibedita Govt General Degree College For Girls, Kolkata, West Bengal, 700027, India
2
Department of Mathematics, Jadavpur University, Kolkata, West Bengal, 700032, India
* e-mail: palsubhajyoti@gmail.com
Received:
25
May
2018
Accepted:
15
April
2019
Published online:
25
April
2019
The present paper considers a three-fluid cosmological model consisting of noninteracting dark matter, dark energy and baryonic matter in the background of the Friedman–Robertson–Walker–Lemaître flat spacetime. It has been assumed that the dark matter takes the form of dust whereas the dark energy is a quintessence (real) scalar field with exponential potential. It has been further assumed that the baryonic matter is a perfect fluid with barotropic equation of states. The field equations for this model takes the form of an autonomous dynamical system after some suitable changes of variables. Then a complete stability analysis is done considering all possible parameter (the adiabatic index of the baryonic matter and the parameter arising from the dark energy potential) values and for both the cases of hyperbolic and non-hyperbolic critical points. For non-hyperbolic critical points, the invariant manifold theory (center manifold approach) is applied. Finally various topologically different phase planes and vector field diagrams are produced and the cosmological interpretation of this model is presented.
© The Author(s), 2019
