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Model-independent constraints on the spatial curvature are not only closely related to important problems, such as the evolution of the universe and properties of dark energy, but also provide a test of the validity of the fundamental Copernican principle. In this paper, with the distance sum rule in the Friedmann–Lemaître–Robertson–Walker metric, we achieve model-independent measurements of the spatial curvature from the latest type Ia supernovae and strong gravitational lensing (SGL) observations. We find that a spatially closed universe is preferred. Moreover, by considering different kinds of velocity dispersion and subsamples, we study possible factors that might affect model-independent estimations for the spatial curvature from SGL observations. It is suggested that the combination of observational data from different surveys might cause a systematic bias, and the tension between the spatially flat universe and SGL observations is alleviated when the subsample only from the Sloan Lens ACS Survey is used or a more complex treatment for the density profile of lenses is considered. [ABSTRACT FROM AUTHOR]

In this paper, we propose to estimate the spatial curvature of the universe and the cosmic opacity in a model-independent way with expansion rate measurements, H(z), and type Ia supernova (SNe Ia). On the one hand, using a nonparametric smoothing method Gaussian process, we reconstruct a function H(z) from opacity-free expansion rate measurements. Then, we integrate the H(z) to obtain distance modulus μH, which is dependent on the cosmic curvature. On the other hand, distances of SNe Ia can be determined by their photometric observations and thus are opacity-dependent. In our analysis, by confronting distance moduli μH with those obtained from SNe Ia, we achieve estimations for both the spatial curvature and the cosmic opacity without any assumptions for the cosmological model. Here, it should be noted that light curve fitting parameters, accounting for the distance estimation of SNe Ia, are determined in a global fit together with the cosmic opacity and spatial curvature to get rid of the dependence of these parameters on cosmology. In addition, we also investigate whether the inclusion of different priors for the present expansion rate (H0: global estimation, 67.74 ± 0.46 km s−1 Mpc−1, and local measurement, 73.24 ± 1.74 km s−1 Mpc−1) exert influence on the reconstructed H(z) and the following estimations of the spatial curvature and cosmic opacity. Results show that, in general, a spatially flat and transparent universe is preferred by the observations. Moreover, it is suggested that priors for H0 matter a lot. Finally, we find that there is a strong degeneracy between the curvature and the opacity. [ABSTRACT FROM AUTHOR]

In this paper, we use a recently compiled data set, which comprises 118 galactic-scale strong gravitational lensing (SGL) systems to constrain the statistical property of the SGL system as well as the curvature of the universe without assuming any fiducial cosmological model. Based on the singular isothermal ellipsoid (SIE) model of the SGL system, we obtain that the constrained curvature parameter is close to zero from the SGL data, which is consistent with the latest result of Planck measurement. More interestingly, we find that the parameter f in the SIE model is strongly correlated with the curvature . Neglecting this correlation in the analysis will significantly overestimate the constraining power of SGL data on the curvature. Furthermore, the obtained constraint on f is different from previous results: (68% confidence level [C.L.]), which means that the standard singular isothermal sphere (SIS) model (f = 1) is disfavored by the current SGL data at more than a C.L. We also divide all of the SGL data into two parts according to the centric stellar velocity dispersion and find that the larger the value of for the subsample, the more favored the standard SIS model is. Finally, we extend the SIE model by assuming the power-law density profiles for the total mass density, , and luminosity density, , and obtain the constraints on the power-law indices: and at a 68% C.L. When assuming the power-law index , this scenario is totally disfavored by the current SGL data, . [ABSTRACT FROM AUTHOR]