Modelling Time-varying Dark Energy with Constraints from Latest Observations

Abstract

We introduce a set of two-parameter models for the dark energy equation of state (EOS) $w(z)$ to investigate time-varying dark energy. The models are classified into two types according to their boundary behaviors at the redshift $z=(0,\infty )$ and their local extremum properties. A joint analysis based on four observations (SNe + BAO + CMB + $H_0$) is carried out to constrain all the models. It is shown that all models get almost the same ${\chi }_{min}^2\simeq 469$ and the cosmological parameters $({\Omega }_M,h,{\Omega }_b{h}^2)$ with the best-fit results $(0.28,0.70,2.24)$, although the constraint results on two parameters $(w_0,w_1)$ and the allowed regions for the EOS $w(z)$ are sensitive to different models and a given extra model parameter. For three of Type I models which have similar functional behaviors with the so-called CPL model, the constrained two parameters $w_0$ and $w_1$ have negative correlation and are compatible with the ones in CPL model, and the allowed regions of $w(z)$ get a narrow node at $z\sim 0.2$. The best-fit results from the most stringent constraints in Model Ia give $(w_0,w_1)=(-0.96_{-0.21}^{+0.26},-0.12_{-0.89}^{+0.61})$ which may compare with the best-fit results $(w_0,w_1)=(-0.97_{-0.18}^{+0.22},-0.15_{-1.33}^{+0.85})$ in the CPL model. For four of Type II models which have logarithmic function forms and an extremum point, the allowed regions of $w(z)$ are found to be sensitive to different models and a given extra parameter. It is interesting to obtain two models in which two parameters $w_0$ and $w_1$ are strongly correlative and appropriately reduced to one parameter by a linear relation $w_1\propto (1+w_0)$.

30 pages, 7 figures

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