Determining cosmological parameters with the latest observational data

Abstract

In this paper, we combine the latest observational data, including the WMAP five-year data (WMAP5), BOOMERanG, CBI, VSA, ACBAR, as well as the baryon acoustic oscillations (BAO) and type Ia supernovae (SN) ``union'' compilation (307 sample), and use the Markov Chain Monte Carlo method to determine the cosmological parameters, such as the equation of state (EoS) of dark energy, the curvature of the universe, the total neutrino mass, and the parameters associated with the power spectrum of primordial fluctuations. In a flat universe, we obtain the tight limit on the constant EoS of dark energy as $w=\ensuremath{-}0.977\ifmmode\pm\else\textpm\fi{}0.056(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.057(\mathrm{sys})$. For the dynamical dark energy models with the time evolving EoS parametrized as ${w}_{\mathrm{de}}(a)={w}_{0}+{w}_{1}(1\ensuremath{-}a)$, we find that the best-fit values are ${w}_{0}=\ensuremath{-}1.08$ and ${w}_{1}=0.368$, while the $\ensuremath{\Lambda}\mathrm{CDM}$ model remains a good fit to the current data. For the curvature of the universe ${\ensuremath{\Omega}}_{k}$, our results give $\ensuremath{-}0.012l{\ensuremath{\Omega}}_{k}l0.009$ (95% C.L.) when fixing ${w}_{\mathrm{de}}=\ensuremath{-}1$. When considering the dynamics of dark energy, the flat universe is still a good fit to the current data, $\ensuremath{-}0.015l{\ensuremath{\Omega}}_{k}l0.018$ (95% C.L.). Regarding the neutrino mass limit, we obtain the upper limits, $\ensuremath{\sum}_{}^{}{m}_{\ensuremath{\nu}}l0.533\text{ }\text{ }\mathrm{eV}$ (95% C.L.) within the framework of the flat $\ensuremath{\Lambda}\mathrm{CDM}$ model. When adding the Sloan Digital Sky Survey Lyman-$\ensuremath{\alpha}$ forest power spectrum data, the constraint on $\ensuremath{\sum}_{}^{}{m}_{\ensuremath{\nu}}$ can be significantly improved, $\ensuremath{\sum}_{}^{}{m}_{\ensuremath{\nu}}l0.161\text{ }\text{ }\mathrm{eV}$ (95% C.L.). However, these limits can be weakened by a factor of 2 in the framework of dynamical dark energy models, due to the obvious degeneracy between neutrino mass and the EoS of the dark energy model. Assuming that the primordial fluctuations are adiabatic with a power law spectrum within the $\ensuremath{\Lambda}\mathrm{CDM}$ model, we find that the upper limit on the ratio of the tensor to scalar is $rl0.200$ (95% C.L.) and the inflationary models with the slope ${n}_{s}\ensuremath{\ge}1$ are excluded at more than $2\ensuremath{\sigma}$ confidence level. However, in the framework of dynamical dark energy models, the allowed region in the parameter space of $({n}_{s},r)$ is enlarged significantly. Finally, we find no strong evidence for the large running of the spectral index.