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Dynamical system analysis of a three fluid cosmological model: an invariant manifold approach

Subhajyoti Pal
(
- Krishnagar Coll.
)
,
Subenoy Chakraborty
(
- Jadavpur U.
)

Apr 25, 2019

13 pages

Published in:

Eur.Phys.J.C 79 (2019) 4, 362

Published: Apr 25, 2019

e-Print:

2002.07588 [gr-qc]

DOI:

10.1140/epjc/s10052-019-6875-4

View in:

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Abstract: (Springer)

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.

Note:

26 pages, 8 figures, 16 tables

cosmological model
fluid
dark energy: potential
field theory: vector
field theory: scalar
critical phenomena
dynamical system
dark matter
equation of state
field equations

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Figures(8)

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