Dynamical Systems Analysis of Various Dark Energy Models

Roy, Nandan (2015) Dynamical Systems Analysis of Various Dark Energy Models. PhD thesis, Indian Institute Of Science Education and Research Kolkata.

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Abstract

From different observations like Type IA supernova and others, it is well established that the universe is in an accelerated expansion phase. But dark energy, the driver of the acceleration, has no unequivocal identification. So there are many models of dark energy. Quintessence models, which are essentially scalar field models are amongst the most favoured models after the cosmological constant. The scalar potential generates a sufficient negative pressure leading to a repulsive gravity which drives the acceleration. Einstein's field equations form a set of nonlinear differential equations. So finding out an exact solution is not always easy. By introducing a set of suitable new variables and a dimensionless time variable, the field equations are written as an autonomous system of equations. Then the fixed points of the system are found out and the stability of the system is analyzed . Stable fixed points are late time attractors and unstable fixed points are repeller. Any heteroclinic solution of the system starts from an unstable fixed point and approaches to a stable fixed point. So one can study the beginning and possible ultimate fate of the universe by finding out the behaviour of the physical parameters near the fixed points. The advantage of this type of analysis is that, with out an exact solution of the field equations, one can discuss the qualitative behavior of the system. In the present thesis, we used dynamical systems analysis to find the qualitative behaviour of various scalar field models of dark energy. Quintessence scalar field models, with and without the tracking condition, are analyzed. With the tracking condition, only one fixed point is of physical interest and some specific potentials can drive the accelerated expansion of the universe. Relaxing the tracking condition and with the boundary values consistent with the present observations the system has been numerically evolved to find the qualitative behaviour of the system. In Chameleon cosmology models the scalar field is coupled to the dark matter. We classified the models in four different classes depending on the combination of chameleon scalar field potentials and the coupling. This analysis includes all sort of combinations of potentials and couplings. Our work gives a list of favoured combinations of potential and coupling on the basis of dynamical systems analysis. Holographic dark energy also attracted attention as it can resolve the coincidence problem. Fixed points of a holographic dark energy model are found out and stability analysis has been done accordingly.

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