Abstract
We study the general property of the evolution of a class of scalar fields with tracking and thawing behaviors. For the tracking solutions, we show explicitly with three different potentials that, independent of initial conditions, there exists a general relation between the equation of state wϕ and the fractional energy density Ωϕ, so that the scalar field follows the same wϕ−Ωϕ trajectory during the evolution. The analytical approximations of the wϕ−Ωϕ trajectories are derived even though the analytical expression depends upon the particular form of the potential. For thawing solutions, a universal wϕ−Ωϕ relation exists and the relation is independent of both the particular form of the potential and the initial condition of the scalar field. Based on the derived wϕ−Ωϕ relation for the thawing models, we derive a tighter upper limit on wϕ′=dwϕ/dlna. The observational data is also used to constrain the thawing potential with the help of the universal wϕ−Ωϕ relation.
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