Model-independent estimations for the curvature from standard candles   and clocks
  Model-independent estimations for the spatial curvature not only provide a test for the fundamental Copernican principle assumption, but also can effectively break the degeneracy between curvature and dark energy properties. In this paper, we propose to achieve model-independent constraints on the spatial curvature from observations of standard candles and standard clocks, without assuming any fiducial cosmology and other priors. We find that, for the popular Union2.1 type Ia supernovae (SNe Ia ) observations, the spatial curvature is constrained to be $\Omega_K=-0.045_{-0.172}^{+0.176}$. For the latest joint light-curve analysis (JLA) of SNe Ia observations, we obtain $\Omega_K=-0.140_{-0.158}^{+0.161}$. It is suggested that these results are in excellent agreement with the spatially flat Universe. Moreover, compared to other approaches aiming for model-independent estimations of spatial curvature, this method also achieves constraints with competitive precision. 
Zhengxiang Li, Guo-Jian Wang, Kai Liao, and Zong-Hong Zhu
astro-ph.CO gr-qc