Abstract
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.
Highlights
A large number of observational data from various sources such as Type Ia Supernova [1,2], CMB anisotropies [4,7], Large Scale Structures [3,5] and Baryon Acoustic Oscillations [6] suggests that we are in a spatially flat universe which after the big bang has undergone two accelerated expansion phases, one occurred before the radiation dominated era and the other one started not too long ago
There the dark energy has been modelled as a scalar field
It has been further assumed that the baryonic matter is a perfect fluid with barotropic equation of states
Summary
A large number of observational data from various sources such as Type Ia Supernova [1,2], CMB anisotropies [4,7], Large Scale Structures [3,5] and Baryon Acoustic Oscillations [6] suggests that we are in a spatially flat universe which after the big bang has undergone two accelerated expansion phases, one occurred before the radiation dominated era and the other one started not too long ago. The motivation to do stability analysis is that after considering all cosmological and observational constraints of data, the stable critical points in our model may depict our present universe as a global attractor. If they do fit with the data of present percentages of dark energy, dark matter and baryonic matter together with radiation in the universe our model would successfully describe the universe. We assume that the potential of the scalar field representing the dark energy is exponential, ie
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