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) on
actual galaxy observations, through a WST analysis of the BOSS DR12 CMASS
dataset. We lay out the detailed procedure on how to capture all necessary
layers of realism for an application on data obtained from a spectroscopic
survey, including the effects of redshift-space anisotropy, non-trivial survey
geometry, the shortcomings of the dataset through a set of systematic weights
and the Alcock-Paczynski distortion effect. 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 theory 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 and 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 in
the range $3-6$ in the case of flat and uninformative priors and by a factor of
$4-28$, when a Big Bang Nucleosynthesis prior is applied on the value of
$\omega_b$. Furthermore, in the latter case, we obtain a 0.6% measurement of
the Hubble constant. Our results are investigative and subject to certain
approximations in our analysis, that we discuss in the text.
