A New Wavelet Scattering Transform-Based Statistic for Cosmological Analysis of Large-Scale Structure

Large-scale structure (LSS) analysis in galaxy surveys is a powerful cosmological probe but is limited by tracer bias, which can obscure underlying information and weaken parameter constraints. Existing methods either model bias or restrict analyses to low-density regions, yet their sensitivity to bias remains poorly understood. We propose a novel method based on the wavelet scattering transform (WST) to distinguish LSS across cosmological models while mitigating tracer bias. Central to our approach are the WST $m$-mode ratios, $R^{\rm wst}$, a new statistical measure, and a high-density apodization preprocessing that smoothly rescales extreme values. We use a reduced chi-square to assess the cosmological parameter constraints and find that $R^{\rm wst}$, in the scale range $j \in [3,7]$, achieves $\chi^2_{\nu, \rm cos} \approx 6$ for cosmology while maintaining $\chi^2_{\nu, \rm bias} \sim 1$--a regime unattained by other statistics. $R^{\rm wst}$ thus provides robust cosmological sensitivity with effective bias mitigation for future surveys.