Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2005-05-25
Gen.Rel.Grav. 38 (2006) 121-135
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
RevTeX4, 11 pages, 3 figures; v2 - corrected fig2
Scientific paper
10.1007/s10714-005-0211-z
We study the Friedmann-Robertson-Walker model with dynamical dark energy modelled in terms of the equation of state $p_{x}=w_{x}(a(z)) \rho_{x}$ in which the coefficient $w_{x}$ is parameterized by the scale factor $a$ or redshift $z$. We use methods of qualitative analysis of differential equations to investigate the space of all admissible solutions for all initial conditions on the two-dimensional phase plane. We show advantages of representing this dynamics as a motion of a particle in the one-dimensional potential $V(a)$. One of the features of this reduction is the possibility of investigating how typical are big rip singularities in the future evolution of the model. The properties of potential function $V$ can serve as a tool for qualitative classification of all evolution paths. Some important features like resolution of the acceleration problem can be simply visualized as domains on the phase plane. Then one is able to see how large is the class of solutions (labelled by the inset of the initial conditions) leading to the desired property.
Hrycyna Orest
Szydlowski Marek
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