Holographic dark energy in a universe with spatial curvature and massive neutrinos: a full Markov Chain Monte Carlo exploration

In this paper, we report the results of constraining the holographic dark energy model with spatial curvature and massive neutrinos, based on a Markov Chain Monte Carlo global fit technique. The cosmic observational data include the full WMAP 7-yr temperature and polarization data, the type Ia supernova data from Union2.1 sample, the baryon acoustic oscillation data from SDSS DR7 and WiggleZ Dark Energy Survey, and the latest measurements of $H_0$ from HST. To deal with the perturbations of dark energy, we adopt the parameterized post-Friedmann method. We find that, for the simplest holographic dark energy model without spatial curvature and massive neutrinos, the phenomenological parameter $c<1$ at more than $4\sigma$ confidence level. The inclusion of spatial curvature enlarges the error bars and leads to $c<1$ only in about $2.5\sigma$ range; in contrast, the inclusion of massive neutrinos does not have significant influence on $c$. We also find that, for the holographic dark energy model with spatial curvature but without massive neutrinos, the $3\sigma$ error bars of the current fractional curvature density $\Omega_{k0}$ are still in order of $10^{-2}$; for the model with massive neutrinos but without spatial curvature, the $2\sigma$ upper bound of the total mass of neutrinos is $\sum m_{\nu} < 0.48$ eV. Moreover, there exists clear degeneracy between spatial curvature and massive neutrinos in the holographic dark energy model, which enlarges the upper bound of $\sum m_{\nu}$ by more than 2 times. In addition, we demonstrate that, making use of the full WMAP data can give better constraints on the holographic dark energy model, compared with the case using the WMAP ``distance priors''.