Constraining dynamical dark energy with a divergence-free parametrization in the presence of spatial curvature and massive neutrinos

In this paper, we report the results of constraining the dynamical dark energy with a divergence-free parameterization, $w(z) = w_{0} + w_{a}(\frac{\ln(2+z)}{1+z}-\ln2)$, in the presence of spatial curvature and massive neutrinos, with the 7-yr WMAP temperature and polarization data, the power spectrum of LRGs derived from SDSS DR7, the Type Ia supernova data from Union2 sample, and the new measurements of $H_0$ from HST, by using a MCMC global fit method. Our focus is on the determinations of the spatial curvature, $\Omega_k$, and the total mass of neutrinos, $\sum m_{\nu}$, in such a dynamical dark energy scenario, and the influence of these factors to the constraints on the dark energy parameters, $w_0$ and $w_a$. We show that $\Omega_k$ and $\sum m_{\nu}$ can be well constrained in this model; the 95% CL limits are: $-0.0153<\Omega_k<0.0167$ and $\sum m_{\nu}<0.56$ eV. Comparing to the case in a flat universe, we find that the error in $w_0$ is amplified by 25.51%, and the error in $w_a$ is amplified by 0.14%; comparing to the case with a zero neutrino mass, we find that the error in $w_0$ is amplified by 12.24%, and the error in $w_a$ is amplified by 1.63%.