Wavelet Moments for Cosmological Parameter Estimation
  Extracting non-Gaussian information from the non-linear regime of structure
formation is key to fully exploiting the rich data from upcoming cosmological
surveys probing the large-scale structure of the universe. However, due to
theoretical and computational complexities, this remains one of the main
challenges in analyzing observational data. We present a set of summary
statistics for cosmological matter fields based on 3D wavelets to tackle this
challenge. These statistics are computed as the spatial average of the complex
modulus of the 3D wavelet transform raised to a power $q$ and are therefore
known as invariant wavelet moments. The 3D wavelets are constructed to be
radially band-limited and separable on a spherical polar grid and come in three
types: isotropic, oriented, and harmonic. In the Fisher forecast framework, we
evaluate the performance of these summary statistics on matter fields from the
Quijote suite, where they are shown to reach state-of-the-art parameter
constraints on the base $\Lambda$CDM parameters, as well as the sum of neutrino
masses. We show that we can improve constraints by a factor 5 to 10 in all
parameters with respect to the power spectrum baseline.
