Going Beyond the Galaxy Power Spectrum: an Analysis of BOSS Data with Wavelet Scattering Transforms

We perform the first application of the wavelet scattering transform (WST) to actual galaxy observations, through a WST analysis of the BOSS DR12 CMASS dataset. We included the effects of redshift-space anisotropy, non-trivial survey geometry, systematic weights, and the Alcock-Paczynski distortion effect, following the commonly adopted steps for the power spectrum analysis. In order to capture the cosmological dependence of the WST, we use galaxy mocks obtained from the state-of-the-art ABACUSSUMMIT simulations, tuned to match the anisotropic correlation function of the BOSS CMASS sample in the redshift range $0.46<z<0.60$. Using our model for the WST coefficients, as well as for the first 2 multipoles of the galaxy power spectrum, that we use as reference, we perform a likelihood analysis of the CMASS data. We obtain the posterior probability distributions of 4 cosmological parameters, $\{\omega_b,\omega_c,n_s,\sigma_8\}$, as well as the Hubble constant, derived from a fixed value of the angular size of the sound horizon at last scattering measured by the Planck satellite, all of which are marginalized over the 7 nuisance parameters of the Halo Occupation Distribution model. The WST is found to deliver a substantial improvement in the values of the predicted $1\sigma$ errors compared to the regular power spectrum, which are tighter by a factor of $3-5$ in the case of flat and uninformative priors and by a factor of $3-8$, when a Big Bang Nucleosynthesis prior is applied on the value of $\omega_b$. Our results are investigative and subject to certain approximations, which we discuss in the text.