Testing the cosmic curvature at high redshifts: the combination of LSST strong lensing systems and quasars as new standard candles

The cosmic curvature, a fundamental parameter for cosmology could hold deep clues to inflation and cosmic origins. We propose an improved model-independent method to constrain the cosmic curvature by combining the constructed Hubble diagram of high-redshift quasars with galactic-scale strong lensing systems expected to be seen by the forthcoming LSST survey. More specifically, the most recent quasar data are used as a new type of standard candles in the range $0.036<z<5.100$, whose luminosity distances can be directly derived from the non-linear relation between X-ray and UV luminosities. Compared with other methods, the proposed one involving the quasar data achieves constraints with higher precision ($\Delta \Omega_k\sim 10^{-2}$) at high redshifts ($z\sim 5.0$). We also investigate the influence of lens mass distribution in the framework of three types of lens models extensively used in strong lensing studies (SIS model, power-law spherical model, and extended power-law lens model), finding the strong correlation between the cosmic curvature and the lens model parameters. When the power-law mass density profile is assumed, the most stringent constraint on the cosmic curvature $\Omega_k$ can be obtained. Therefore, the issue of mass density profile in the early-type galaxies is still a critical one that needs to be investigated further.