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.
Two types of interacting dark energy models are investigated using the type Ia supernova (SNIa), observational $H(z)$ data (OHD), cosmic microwave background (CMB) shift parameter and the secular Sandage-Loeb (SL) test. We find that the inclusion of
SL test can obviously provide more stringent constraint on the parameters in both models. For the constant coupling model, the interaction term including the SL test is estimated at $delta=-0.01 pm 0.01 (1sigma) pm 0.02 (2sigma)$, which has been improved to be only a half of original scale on corresponding errors. Comparing with the combination of SNIa and OHD, we find that the inclusion of SL test directly reduces the best-fit of interaction from 0.39 to 0.10, which indicates that the higher-redshift observation including the SL test is necessary to track the evolution of interaction. For the varying coupling model, we reconstruct the interaction $delta (z)$, and find that the interaction is also negative similar as the constant coupling model. However, for high redshift, the interaction generally vanishes at infinity. The constraint result also shows that the $Lambda$CDM model still behaves a good fit to the observational data, and the coincidence problem is still quite severe. However, the phantom-like dark energy with $w_X<-1$ is slightly favored over the $Lambda$CDM model.
