Galaxy Clustering Analysis with SimBIG and the Wavelet Scattering Transform

Abstract

The non-Gaussisan spatial distribution of galaxies traces the large-scale structure of the Universe and therefore constitutes a prime observable to constrain cosmological parameters. We conduct Bayesian inference of the $\Lambda$CDM parameters ${\Omega }_m$, ${\Omega }_b$, $h$, $n_s$, and ${\sigma }_8$ from the BOSS CMASS galaxy sample by combining the wavelet scattering transform (WST) with a simulation-based inference approach enabled by the $\mathrm{S}\mathrm{IM}\mathrm{BIG}$ forward model. We design a set of reduced WST statistics that leverage symmetries of redshift-space data. Posterior distributions are estimated with a conditional normalizing flow trained on 20,000 simulated $\mathrm{S}\mathrm{IM}\mathrm{BIG}$ galaxy catalogs with survey realism. We assess the accuracy of the posterior estimates using simulation-based calibration and quantify generalization and robustness to the change of forward model using a suite of 2,000 test simulations. When probing scales down to $k_{\max }=0.5h/\text{Mpc}$, we are able to derive accurate posterior estimates that are robust to the change of forward model for all parameters, except ${\sigma }_8$. We mitigate the robustness issues with ${\sigma }_8$ by removing the WST coefficients that probe scales smaller than $k\sim 0.3h/\text{Mpc}$. Applied to the BOSS CMASS sample, our WST analysis yields seemingly improved constraints obtained from a standard PT-based power spectrum analysis with $k_{\max }=0.25h/\text{Mpc}$ for all parameters except $h$. However, we still raise concerns on these results. The observational predictions significantly vary across different normalizing flow architectures, which we interpret as a form of model misspecification. This highlights a key challenge for forward modeling approaches when using summary statistics that are sensitive to detailed model-specific or observational imprints on galaxy clustering.

11+5 pages, 8+2 figures, published in Physical Review D

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