We present a new parameterization of quintessence potentials for dark energy based directly upon the dynamical properties of the equations of motion. Such parameterization arises naturally once the equations of motion are written as a dynamical system in terms of properly defined polar variables. We have identified two different classes of parameters, and we dubbed them as dynamical and passive parameters. The dynamical parameters appear explicitly in the equations of motion, but the passive parameters play just a secondary role in their solutions. The new approach is applied to the so-called thawing potentials and it is argued that only three dynamical parameters are sufficient to capture the evolution of the quintessence fields at late times. This work reconfirms the arbitrariness of the quintessence potentials as the recent observational data fail to constrain the dynamical parameters. 95.36.+x arXiv:1803.09204v2 [gr-qc]

The present work deals with a dynamical systems study of quintessence potentials leading to the present accelerated expansion of the universe. The principal interest is to check for late time attractors which give an accelerated expansion for the universe. Two examples are worked out, namely the exponential and the power-law potentials.

With the tracking condition, the stability of quintessence solutions are examined. It is found that there is only one physically relevant fixed point for the system generically. Two specific examples of quintessence potentials are worked out in the frame work.Comment: 10 pages, 3 figures; Accepted for publication in Gen. Relativ. Gravi

The stability criteria for the generalized Brans-Dicke cosmology in a spatially flat, homogeneous and isotropic cosmological model is discussed in the presence of a perfect fluid. The generalization comes through the channel that the Brans-Dicke coupling parameter ω is allowed to be a function of the scalar field φ. This generalization can lead to a host of scalar-tensor theories of gravity for various choices of ω = ω(φ). A very interesting general result has been found. Excepting for the case of a radiation distribution as the choice of the fluid, all other solutions find a natural habitat in the corresponding solutions in general relativity in an infinite ω limit. For the radiation distribution, the dependence of stability on ω is a bit obscure. If a scalar potential, function of the Brans-Dicke scalar field, is added to the action, the requirement of an infinite ω for stability is relaxed for a matter distribution with a non-zero trace whereas it becomes a possibility for a radiation distribution.PACS numbers: 98.80.-k; 95.36.+x

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