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The lensing effect of the cosmic microwave background (CMB) is a powerful tool for our study of the distribution of matter in the universe. The quadratic estimator (QE) method, which is widely used to reconstruct lensing potential, has been known to be suboptimal for the low noise level polarization data from next-generation CMB experiments. To improve the performance of the reconstruction, other methods, such as the maximum-likelihood estimator and machine-learning algorithms, have been developed. In this work, we present a deep convolutional neural network model named the Residual Dense Local Feature U-net (RDLFUnet) for reconstructing the CMB lensing convergence field. By simulating lensed CMB data with different noise levels to train and test network models, we find that for noise levels less than 5 μ K-arcmin, RDLFUnet can recover the input gravitational potential with a higher signal-to-noise ratio than the previous deep-learning and traditional QE methods at almost the entire observation scale. [ABSTRACT FROM AUTHOR]

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]

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]