The phase space analysis of cosmological parameters $Omega_{phi}$ and $gamma_{phi}$ is given. Based on this, the well-known quintessence cosmology is studied with an exponential potential $V(phi)=V_{0}exp(-lambdaphi)$. Given observational data, the c
urrent state of universe could be pinpointed in the phase diagrams, thus making the diagrams more informative. The scaling solution of quintessence usually is not supposed to give the cosmic accelerating expansion, but we prove it could educe the transient acceleration. We also find that the differential equations of system used widely in study of scalar field are incomplete, and then a numerical method is used to figure out the range of application.
Recently a $f(T)$ gravity based on the modification of the teleparallel gravity was proposed to explain the accelerated expansion of the universe without the need of dark energy. We use observational data from Type Ia Supernovae, Baryon Acoustic Osci
llations, and Cosmic Microwave Background to constrain this $f(T)$ theory and reconstruct the effective equation of state and the deceleration parameter. We obtain the best-fit values of parameters and find an interesting result that the $f(T)$ theory considered here allows for the accelerated Hubble expansion to be a transient effect.
