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

TL;DR

The paper introduces a novel bias-robust framework for cosmological analysis of large-scale structure based on 3D wavelet scattering transform (WST) coefficients. Central to the method are the WST $m$-mode ratios $R^{\rm wst}$ (and a secondary $R_2^{\rm wst}$) designed to cancel linear tracer bias while preserving cosmological information, augmented by a high-density apodization preprocessing. Using CosmicGrowth N-body simulations, the authors show that, for $j\in[3,7]$ and $l\in[1,2]$, $R^{\rm wst}$ achieves $\chi^2_{\nu,\rm cos} \approx 6$ with $\chi^2_{\nu,\rm bias} \sim 0.3$–$1$, a regime not reached by traditional statistics such as $P(k)$ or $P_{\rm norm}(k)$ or by $m$-averaged WST coefficients. The results indicate that this approach provides strong cosmological sensitivity while effectively mitigating tracer-bias effects, offering a practical tool for upcoming Stage-IV galaxy surveys; future work will address more realistic galaxy models, survey systematics, and combined statistics to further enhance discriminative power.

Abstract

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 $χ^2_{ν, \rm cos} \approx 6$ for cosmology while maintaining $χ^2_{ν, \rm bias} \sim 1$--a regime unattained by other statistics. $R^{\rm wst}$ thus provides robust cosmological sensitivity with effective bias mitigation for future surveys.

Figures (5)

• Figure 1: Resulting 1D projection of first order WST component images (the same region from figure \ref{['fig:b']}) are computed with $j$ ranging from 0 to 7 and fixed $l = 1$, $m=1$, for the $\texttt{WMAP}$ dataset with the high-density apodization. As $j$ increases, the results reveal progressively larger-scale structures, demonstrating that different $j$ values extract features at different spatial scales. Since the value range of each component varies significantly, each image is rescaled by min-max Normalization to make the values dimensionless.
• Figure 2: Tanh-based decay profiles for different values of $k$. We adopt $k=0.4$ in this study.
• Figure 3: A comparison of the overdensity fields before (left) and after (right) applying high-density apodization across different datasets. Each panel shows a 1D projection of the field, computed on a $300^2$ grid spanning 300 ${\rm Mpc}/h$ per side, with a slice thickness of $150~{\rm Mpc}/h$. The first, second, and third rows show slices from the mWMAP, WMAP, and Planck datasets, respectively. As observed, the apodization scheme suppresses high-density peaks by shifting them toward the mean density, while leaving low-density regions largely unchanged.
• Figure 4: Results for $\chi^2$ (left) and $\chi^2_{\nu}$ (right), with eight cases corresponding to different ranges of $j$, while keeping $l \in [1,2]$ fixed. The results for the $j$ ranges from $[0,7]$ to $[7,7]$ are shown respectively, corresponding to different $R^{\mathrm {wst}}$ measurements, leading to different $\chi^2$ and $\chi^2_{\nu}$ values. Each panel compares the results with (triangle) and without (solid dot) the high-density apodization scheme.
• Figure 5: Reduced chi-squared values, $\chi^2_\nu$, for cosmological parameters (left) and tracer bias (right), evaluated using various statistical summaries: WST $m$-mode ratios, $m$-averaged WST coefficients, the power spectrum, and the normalized power spectrum, all with the high-density apodization. The dotted line marks $\chi^2_\nu = 1$ (ideal fit), and each measurement includes its associated $2\sigma$ error bar. The red shaded regions indicate the chosen $R^{\rm wst}$ for $j \in [3,7]$, which offer high cosmological sensitivity with reduced tracer bias dependence.