  As weak lensing surveys become deeper, they reveal more non-Gaussian aspects
of the convergence field which can only be extracted using statistics beyond
the power spectrum. In Cheng et al. (2020) we showed that the scattering
transform, a novel statistic borrowing mathematical concepts from convolutional
neural networks, is a powerful tool for cosmological parameter estimation in
the non-Gaussian regime. Here, we extend that analysis to explore its
sensitivity to dark energy and neutrino mass parameters with weak lensing
surveys. We first use image synthesis to show visually that, compared to the
power spectrum and bispectrum, the scattering transform provides a better
statistical vocabulary to characterize the perceptual properties of lensing
mass maps. We then show that it is also better suited for parameter inference:
(i) it provides higher sensitivity in the noiseless regime, and (ii) at the
noise level of Rubin-like surveys, though the constraints are not significantly
tighter than those of the bispectrum, the scattering coefficients have a more
Gaussian sampling distribution, which is an important property for likelihood
parametrization and accurate cosmological inference. We argue that the
scattering coefficients are preferred statistics considering both constraining
power and likelihood properties.
