Csst Strong Lensing Achieves Cosmological Constraints with Hundreds of DSPL Systems

Researchers are increasingly turning to double source plane strong lensing (DSPL) systems as a powerful, independent method for refining our understanding of the universe’s fundamental parameters. Bei-Chen Wu, Xiaoyue Cao (from the Institute for Astrophysics, Zhengzhou University), and Nan Li, alongside Yan Gong, Shenzhe Cui, and Di Wu, investigate how the forthcoming Chinese Space Station Telescope (CSST) can best exploit these systems for cosmological inference. Their work simulates realistic DSPLs to determine how CSST’s different survey modes , Wide, Deep, and Ultra-Deep Fields , impact the precision with which we can measure cosmological constants. This research is significant because it identifies that deeper observations, particularly within the Ultra-Deep Field, and systems exhibiting smaller Einstein radius ratios, will dramatically enhance CSST’s ability to constrain cosmological parameters, paving the way for more accurate measurements of dark energy and the universe’s expansion rate.

This research investigates how varying signal-to-noise ratios (SNR) and Einstein radius ratios, denoted as β−1 parameters, impact cosmological inference using DSPLs under different CSST survey modes: Wide Field (WF), Deep Field (DF), and Ultra-Deep Field (UDF). The team achieved a detailed simulation and modelling of mock lenses, employing Singular Isothermal Ellipsoid (SIE) mass profiles and Sérsic sources meticulously tailored to CSST specifications, allowing for a robust assessment of observational constraints. Assuming a flat wCDM universe with fiducial values of Ωm = 0.30966 and w = −1, and utilising uniform priors of Ωm ∈[0, 1] and w ∈[−2, −1/3), the study reveals a substantial increase in the constraining power on cosmological parameters as survey depth increases.

For a typical DSPL system exhibiting two prominent arcs and a moderate β−1 value of 1.17, the constraints on the dark energy equation of state (w) and matter density (Ωm) improved dramatically from (w = −1.28+0.64 −1.00, Ωm = 0.50+0.28 −0.32) in the WF mode to (w = −1.59+0.63 −0.32, Ωm = 0.42+0.15 −0.06) in the UDF mode. This significant enhancement underscores the critical role of survey depth in maximising the cosmological information extracted from DSPL systems. Furthermore, experiments show that DSPL systems with smaller β values consistently yield tighter cosmographic constraints, suggesting a preference for systems with specific geometrical properties. The research establishes that DSPL systems identified through UDF observations, particularly those characterised by small β values, represent the most promising candidates for early-stage cosmological studies with CSST.
This finding directs observational strategies towards prioritising these systems for detailed analysis, optimising the potential for groundbreaking cosmological discoveries. The work opens exciting possibilities for leveraging the anticipated wealth of DSPL data from CSST to refine our understanding of dark energy and the universe’s expansion history. By meticulously simulating and modelling these lensing systems, scientists prove the feasibility of achieving unprecedented precision in cosmological parameter estimation, complementing existing probes and potentially resolving long-standing mysteries in cosmology. To assess the impact of signal-to-noise ratio (SNR) and Einstein radius ratio (β−1) on cosmographic inference, the research team simulated mock lenses employing Singular Isothermal Ellipsoid (SIE) mass profiles and Sérsic sources, specifically configured to match CSST observational characteristics. These simulated lenses were then modelled to determine how accurately cosmological parameters could be recovered under different CSST survey modes: Wide Field (WF), Deep Field (DF), and Ultra-Deep Field (UDF). The study assumed a flat wCDM universe with fiducial values of Ωm = 0.30966 and w = −1, applying uniform priors of Ωm ∈[0, 1] and w ∈[−2, −1/3).

Researchers meticulously constructed the mock DSPL systems, ensuring each featured two prominent arcs and a moderate β−1 value of 1.17, to represent realistic observational scenarios. By systematically varying the survey depth, from WF to DF to UDF, the team quantified the resulting improvements in constraining cosmological parameters, demonstrating a clear correlation between depth and precision. Experiments revealed that constraints on the dark energy equation of state parameter (w) and matter density (Ωm) improved significantly with increased survey depth; for the representative DSPL system, (w, Ωm) evolved from (−1.28+0.64 −1.00, 0.50+0.28 −0.32) in the WF mode to (−1.59+0.63 −0.32, 0.42+0.15 −0.06) in the UDF mode. This methodological approach enabled a precise quantification of the gains achievable with deeper observations.

The team further discovered that DSPL systems exhibiting smaller β values consistently yielded tighter cosmographic constraints, highlighting their superior potential for cosmological studies. This work pioneered a robust simulation framework to predict the performance of DSPL systems with CSST, allowing researchers to identify optimal survey strategies. The study harnessed the geometrical advantages of DSPLs, particularly the β ratio, to probe the distant universe independently of the local distance ladder. The research team meticulously simulated and modelled mock lenses, employing Singular Isothermal Ellipsoid (SIE) mass profiles and Sérsic sources tailored to CSST specifications, to investigate the impact of signal-to-noise ratios (SNR) and Einstein radius ratios on cosmographic inference across different CSST survey modes, Wide Field (WF), Deep Field (DF), and Ultra-Deep Field (UDF). Assuming a flat CDM universe with fiducial values of Ωm = 0.30966 and w = -1, the study revealed a substantial increase in constraining power on cosmological parameters with increasing survey depth. Experiments demonstrated that for a representative DSPL system exhibiting two prominent arcs and a moderate Einstein radius ratio, the constraints on Ωm improved from 0.09 in the WF mode to 0.03 in the UDF mode, a threefold enhancement in precision.

Furthermore, data shows that systems characterised by smaller Einstein radius ratios consistently yielded tighter cosmographic constraints, indicating their superior suitability for cosmological studies. The team measured the angular diameter distance using the equation D(zi, zj) = c/H0, confirming its crucial role in determining the cosmological scaling factor β, which serves as a reliable bridge to constrain cosmological parameters. Results demonstrate that the precision with which β can be measured is directly linked to the signal-to-noise ratio and spatial resolution of the imaging data, alongside the accuracy of redshift measurements. To generate realistic mock images, the researchers modelled lens mass distributions with analytical SIE profiles and source surface brightness with Sérsic profiles, carefully isolating the effect of the Einstein radius ratio.

The modelling incorporated the horizontal and vertical reduced deflection angles, calculated using equations (5) and (6), to accurately represent the lensing effects. Tests prove that DSPL systems identified in UDF observations, especially those with small Einstein radius ratios, are the most promising candidates for early-stage cosmological studies with CSST. The breakthrough delivers a basis for future discussions on how DSPLs can be exploited by CSST and other major facilities under various observing conditions and within different DSPL-based inference frameworks. Their research focused on simulating and modelling mock lenses to assess how signal-to-noise ratios (SNR) and Einstein radius ratios impact the precision of cosmographic inference under different CSST survey modes, Wide Field, Deep Field, and Ultra-Deep Field. The simulations employed Singular Isothermal Ellipsoid (SIE) mass profiles and Sérsic sources, tailored to CSST specifications, assuming a flat CDM universe with specific values for cosmological parameters. The findings reveal a significant improvement in constraining power on cosmological parameters with increasing survey depth; for a typical DSPL system, constraints on parameters improved substantially from the Wide Field to the Ultra-Deep Field mode.

Systems exhibiting smaller values also yielded tighter cosmographic constraints, suggesting these are particularly valuable for early cosmological studies with CSST. The authors acknowledge limitations stemming from simplified lensing models and the neglect of certain systematic uncertainties, such as lens light contamination and environmental effects. This work establishes that DSPL systems observed in the Ultra-Deep Field, especially those with smaller Einstein radius ratios, represent the most promising targets for initial cosmological investigations using CSST. The research highlights the importance of survey depth in maximising the cosmological information obtainable from DSPLs. Future research could explore how DSPLs can be exploited by CSST and other facilities under various observing conditions and within different inference frameworks, building upon these initial findings to refine cosmological measurements.