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.
The varying speed of light (VSL) theory is controversial. It succeeds in explaining some cosmological problems, but on the other hand it is excluded by mainstream physics because it will shake the foundation of physics. In the present paper, we devot
e ourselves to test whether the speed of light is varying from the observational data of the type Ia Supernova, Baryon Acoustic Oscillation, Observational $H(z)$ data and Cosmic Microwave Background (CMB). We select the common form $c(t)=c_0a^n(t)$ with the contribution of dark energy and matter, where $c_0$ is the current value of speed of light, $n$ is a constant, and consequently construct a varying speed of light dark energy model (VSLDE). The combined observational data show a much trivial constraint $n=-0.0033 pm 0.0045$ at 68.3% confidence level, which indicates that the speed of light may be a constant with high significance. By reconstructing the time-variable $c(t)$, we find that the speed of light almost has no variation for redshift $z < 10^{-1}$. For high-$z$ observations, they are more sensitive to the VSLDE model, but the variation of speed of light is only in order of $10^{-2}$. We also introduce the geometrical diagnostic $Om (z)$ to show the difference between the VSLDE and $Lambda$CDM model. The result shows that the current data are difficult to differentiate them. All the results show that the observational data favor the constant speed of light.
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.
