Precise Cosmological Constraints from BOSS Galaxy Clustering with a Simulation-Based Emulator of the Wavelet Scattering Transform

We perform a reanalysis of the BOSS CMASS DR12 galaxy dataset using a simulation-based emulator for the Wavelet Scattering Transform (WST) coefficients. Moving beyond our previous works, which laid the foundation for the first galaxy clustering application of this estimator, we construct a neural net-based emulator for the cosmological dependence of the WST coefficients and the 2-point correlation function multipoles, trained from the state-of-the-art suite of \textsc{AbacusSummit} simulations combined with a flexible Halo Occupation Distribution (HOD) galaxy model. In order to confirm the accuracy of our pipeline, we subject it to a series of thorough internal and external mock parameter recovery tests, before applying it to reanalyze the CMASS observations in the redshift range $0.46<z<0.57$. We find that a joint WST + 2-point correlation function likelihood analysis allows us to obtain marginalized 1$\sigma$ errors on the $\Lambda$CDM parameters that are tighter by a factor of $2.5-6$, compared to the 2-point correlation function, and by a factor of $1.4-2.5$ compared to the WST-only results. This corresponds to a competitive $0.9\%$, $2.3\%$ and $1\%$ level of determination for parameters $\omega_c$, $\sigma_8$ $\&$ $n_s$, respectively, and also to a $0.7\%$ $\&$ $2.5 \%$ constraint on derived parameters h and $f(z)\sigma_8(z)$, in agreement with the \textit{Planck} 2018 results. Our results reaffirm the constraining power of the WST and highlight the exciting prospect of employing higher-order statistics in order to fully exploit the power of upcoming Stage-IV spectroscopic observations.