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Model-independent estimations for the spatial curvature of the universe not only provide a test for the fundamental assumption of the Copernican principle, 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 or other priors. We find that, for the popular Union2.1 observations of Type Ia supernovae (SNe Ia), the spatial curvature is constrained to be . For the latest joint light-curve analysis of SNe Ia observations, we obtain . It is suggested that these results are in excellent agreement with a spatially flat universe. Moreover, compared to other approaches aiming for model-independent estimations of spatial curvature, this method also achieves constraints with competitive precision. [ABSTRACT FROM AUTHOR]

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]

We present a new model-independent strategy for testing the Friedmann–Lemaître–Robertson–Walker (FLRW) metric and constraining cosmic curvature, based on future time-delay measurements of strongly lensed quasar-elliptical galaxy systems from the Large Synoptic Survey Telescope and supernova observations from the Dark Energy Survey. The test only relies on geometric optics. It is independent of the energy contents of the universe and the validity of the Einstein equation on cosmological scales. The study comprises two levels: testing the FLRW metric through the distance sum rule (DSR) and determining/constraining cosmic curvature. We propose an effective and efficient (redshift) evolution model for performing the former test, which allows us to concretely specify the violation criterion for the FLRW DSR. If the FLRW metric is consistent with the observations, then on the second level the cosmic curvature parameter will be constrained to ∼0.057 or ∼0.041 (1σ), depending on the availability of high-redshift supernovae, which is much more stringent than current model-independent techniques. We also show that the bias in the time-delay method might be well controlled, leading to robust results. The proposed method is a new independent tool for both testing the fundamental assumptions of homogeneity and isotropy in cosmology and for determining cosmic curvature. It is complementary to cosmic microwave background plus baryon acoustic oscillation analyses, which normally assume a cosmological model with dark energy domination in the late-time universe. [ABSTRACT FROM AUTHOR]