Constrains of dark energy (DE) at high redshift from current and mock future observational data are obtained. It is found that present data give poor constraints of DE even beyond redshift z=0.4, and mock future 2298 type Ia supernove data only give
a little improvement of the constraints. We analyze in detail why constraints of DE decrease rapidly with the increasing of redshift. Then we try to improve the constraints of DE at high redshift. It is shown that the most efficient way is to improve the error of observations.
The model-independent piecewise parametrizations (0-spline, linear-spline and cubic-spline) are used to estimate constraints of equation of state of dark energy ($w_{de}$) from current observational data (including SNIa, BAO and Hubble parameter) and
the simulated future data. A combination of fitting results of $w_{de}$ from these three spline methods reveal essential properties of real equation of state $w_{de}$. It is shown that $w_{de}$ beyond redshift $zsim0.5$ is poorly constrained from current data, and the mock future $sim2300$ supernovae data give poor constraints of $w_{de}$ beyond $zsim1$. The fitting results also indicate that there might exist a rapid transition of $w_{de}$ around $zsim0.5$. The difference between three spline methods in reconstructing and constraining $w_{de}$ has also been discussed.
To constrain cosmological parameters, one often makes a joint analysis with different combinations of observational data sets. In this paper we take the figure of merit (FoM) for Dark Energy Task Force fiducial model (CPL model) to estimate goodness
of different combinations of data sets, which include 11 widely-used observational data sets (Type Ia Supernovae, Observational Hubble Parameter, Baryon Acoustic Oscillation, Cosmic Microwave Background, X-ray Cluster Baryon Mass Fraction, and Gamma-Ray Bursts). We analyze different combinations and make a comparison for two types of combination based on two types of basic combinations, which are often adopted in the literatures. We find two sets of combinations, which have strong ability to constrain the dark energy parameters, one has the largest FoM, the other contains less observational data with a relative large FoM and a simple fitting procedure.
Quintessence field is a widely-studied candidate of dark energy. There is tracker solution in quintessence models, in which evolution of the field $phi$ at present times is not sensitive to its initial conditions. When the energy density of dark ener
gy is neglectable ($Omega_phill1$), evolution of the tracker solution can be well analysed from tracker equation. In this paper, we try to study evolution of the quintessence field from full tracker equation, which is valid for all spans of $Omega_phi$. We get stable fixed points of $w_phi$ and $Omega_phi$ (noted as $hat w_phi$ and $hatOmega_phi$) from the full tracker equation, i.e., $w_phi$ and $Omega_phi$ will always approach $hat w_phi$ and $hatOmega_phi$ respectively. Since $hat w_phi$ and $hatOmega_phi$ are analytic functions of $phi$, analytic relation of $hat w_phisimhatOmega_phi$ can be obtained, which is a good approximation for the $w_phisimOmega_phi$ relation and can be obtained for the most type of quintessence potentials. By using this approximation, we find that inequalities $hat w_phi<w_phi$ and $hatOmega_phi<Omega_phi$ are statisfied if the $w_phi$ (or $hat w_phi$) is decreasing with time. In this way, the potential $U(phi)$ can be constrained directly from observations, by no need of solving the equations of motion numerically.
We investigate dynamical behavior of the equation of state of dark energy $w_{de}$ by employing the linear-spline method in the region of low redshifts from observational data (SnIa, BAO, CMB and 12 $H(z)$ data). The redshift is binned and $w_{de}$ i
s approximated by a linear expansion of redshift in each bin. We leave the divided points of redshift bins as free parameters of the model, the best-fitted values of divided points will represent the turning positions of $w_{de}$ where $w_{de}$ changes its evolving direction significantly (if there exist such turnings in our considered region). These turning points are natural divided points of redshift bins, and $w_{de}$ between two nearby divided points can be well approximated by a linear expansion of redshift. We find two turning points of $w_{de}$ in $zin(0,1.8)$ and one turning point in $zin (0,0.9)$, and $w_{de}(z)$ could be oscillating around $w=-1$. Moreover, we find that there is a $2sigma$ deviation of $w_{de}$ from -1 around $z=0.9$ in both correlated and uncorrelated estimates.
It is possible that there exist some interactions between dark energy (DE) and dark matter (DM), and a suitable interaction can alleviate the coincidence problem. Several phenomenological interacting forms are proposed and are fitted with observation
s in the literature. In this paper we investigate the possible interaction in a way independent of specific interacting forms by use of observational data (SNe, BAO, CMB and Hubble parameter). We divide the whole range of redshift into a few bins and set the interacting term $delta(z)$ to be a constant in each redshift bin. We consider four parameterizations of the equation of state $w_{de}$ for DE and find that $delta(z)$ is likely to cross the non-interacting ($delta=0$) and have an oscillation form. It suggests that to study the interaction between DE and DM, more general phenomenological forms of the interacting term should be considered.
