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 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 nonlinear transformations that are sensitive to non-Gaussianity in spatial density distributions. In order to assess its applicability in the context of large-scale structure surveys, we apply the WST on the 3D overdensity field obtained by the Quijote simulations, out of which we extract the Fisher information in six cosmological parameters. WST delivers a large improvement in the marginalized errors on all parameters, ranging between 1. 2-4 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.