Model-independent Constraints on Cosmic Curvature: Implication from Updated Hubble Diagram of High-redshift Standard Candles

Abstract

The cosmic curvature (Ω_k) is a fundamental parameter for cosmology. In this paper, we propose an improved model-independent method to constrain the cosmic curvature, which is geometrically related to the Hubble parameter H(z) and luminosity distance D_L(z). Using the currently largest H(z) sample from the well-known cosmic chronometers, as well as the luminosity distance D_L(z) from the relation between the UV and X-ray luminosities of 1598 quasars and the newly compiled Pantheon sample including 1048 SNe Ia, 31 independent measurements of the cosmic curvature Ω_k(z) can be expected covering the redshift range of 0.07 < z < 2. Our estimation of Ω_k(z) is fully compatible with flat universe at the current level of observational precision. Meanwhile, we find that, for the Hubble diagram of 1598 quasars as a new type of standard candle, the spatial curvature is constrained to be Ω_k = 0.08 ± 0.31. For the latest Pantheon sample of SNe Ia observations, we obtain Ω_k = - 0.02 ± 0.14. Compared to other approaches aiming for model-independent estimations of spatial curvature, our analysis also achieves constraints with competitive precision. More interestingly, it is suggested that the reconstructed curvature Ω_k is negative in the high-redshift region, which is also consistent with the results from the model-dependent constraints in the literature. Such findings are confirmed by our reconstructed evolution of Ω_k(z), in the framework of a model-independent method of Gaussian processes (GP) without assuming a specific form.