CSST Strong Lensing Preparation: Cosmological constraints from double-source-plane strong lensing systems in era of CSST

Double source plane strong lensing (DSPL) systems offer a robust, independent probe of cosmological parameters. The Chinese Space Station Telescope (CSST) is expected to discover hundreds of DSPLs, yet the survey modes and system configurations that best enable cosmological inference remain uncertain. To investigate the impact of varying signal-to-noise ratios (SNR) and Einstein radius ratios of DSPLs (denoted as $\beta^{-1}$ parameters) on cosmographic inference under different CSST survey modes (Wide Field (WF), Deep Field (DF), and Ultra-Deep Field (UDF)), we simulate and model mock lenses with Singular Isothermal Ellipsoid (SIE) mass profiles and S\'ersic sources whose image properties are tailored to CSST specifications. Assuming a flat $w$CDM universe with fiducial values $\Omega_{\rm m} = 0.30966$ and $w = -1$, and uniform priors of $\Omega_{\rm m} \in [0, 1]$ and $w \in [-2, -1/3$), we find that the constraining power on cosmological parameters for a given DSPL system increases significantly with survey depth. For a representative DSPL system with two prominent arcs and a moderate $\beta^{-1}=1.17$, the constraints on ($w, \Omega_{\rm m}$) improve from ($-1.28_{-1.00}^{+0.64}, 0.50_{-0.32}^{+0.28}$) in the WF to ($-1.59_{-0.32}^{+0.63}, 0.42_{-0.06}^{+0.15}$) in the UDF. Furthermore, we find that systems with smaller $\beta$ values yield tighter cosmographic constraints. We conclude that DSPL systems identified in UDF observations, particularly those with small $\beta$, are the most promising candidates for early-stage cosmological studies with CSST.