Towards an Optimal Estimation of Cosmological Parameters with the
  Wavelet Scattering Transform
  Optimal extraction of the non-Gaussian information encoded in the Large-Scale
Structure (LSS) of the universe lies at the forefront of modern precision
cosmology. We propose achieving this task through the use of the Wavelet
Scattering Transform (WST), which subjects an input field to a layer of
non-linear transformations that are sensitive to non-Gaussianity in spatial
density distributions through a generated set of WST coefficients. In order to
assess its applicability in the context of LSS surveys, we apply the WST on the
3D overdensity field obtained by the Quijote simulations, out of which we
extract the Fisher information in 6 cosmological parameters. It is subsequently
found to deliver a large improvement in the marginalized errors on all
parameters, ranging between $1.2-4\times$ tighter than the corresponding ones
obtained from the regular 3D cold dark matter + baryon power spectrum, as well
as a $50 \%$ improvement over the neutrino mass constraint given by the marked
power spectrum. Through this first application on 3D cosmological fields, we
demonstrate the great promise held by this novel statistic and set the stage
for its future application to actual galaxy observations.
