Re-examining the role of curvature in the slowing down acceleration scenario

Abstract

By incorporating the curvature ${\ensuremath{\Omega}}_{k}$ as a free parameter, it has been found that the tension between the high redshift cosmic microwave background (CMB) shift parameter $R({z}^{*})$ data and the low redshift Type Ia supernova (SNIa) and baryonic acoustic oscillation (BAO) data from the combination of Sloan Digital Sky Survey (SDSS) and Two-Degree Field Galaxy Redshift Survey (2dFGRS) can be ameliorated, and both $\mathrm{SNIa}+\mathrm{BAO}$ and $\mathrm{SNIa}+\mathrm{BAO}+\mathrm{CMB}$ favor that the decelerating parameter $q(z)$ shows a rapid variation in the sign at the small redshift. In this paper, with the Monte Carlo Markov chain method, we re-examine the evolutionary behavior of $q(z)$ using the latest observational data including the Union2 SNIa, BAO, and CMB data ($R({z}^{*})$, ${l}_{A}({z}^{*})$, ${z}^{*}$) from Wilkinson Microwave Anisotropy Probe 7-yr (WMAP7). For the BAO data, four different data sets obtained from the Two-Degree Field Galaxy Survey, the combination of SDSS and 2dFGRS, the WiggleZ Dark Energy Survey, and the Baryonic Oscillation Spectroscopic Survey, are used. Except for the spatially flat case constrained by $\mathrm{SNIa}+\mathrm{\text{the WiggleZ}}\text{ }\mathrm{BAO}$ data, both SNIa and other $\mathrm{BAO}+\mathrm{SNIa}$ favor that the present cosmic acceleration is slowing down irrespective of whether the spatial curvature is included or not. However, once the WMAP7 CMB data is included, observations favor strongly the Lambda cold dark matter model, a spatially flat universe, and a speeding-up of the cosmic acceleration. Therefore, the inclusion of spatial curvature seems to have no effect on alleviating the tension between $\mathrm{SNIa}+\mathrm{BAO}$ and CMB in clear contrast to the previous work in the literature.