Starlet higher order statistics for galaxy clustering and weak lensing

We present a first application to photometric galaxy clustering and weak lensing of wavelet-based multi-scale (beyond two points) summary statistics: starlet peak counts and starlet ℓ 1 -norm. Peak counts are the local maxima in the map, and ℓ 1 -norm is computed via the sum of the absolute values of the starlet (wavelet) decomposition coefficients of a map, providing a fast multi-scale calculation of the pixel distribution, encoding the information of all pixels in the map. We employ the cosmo-SLICS simulations sources and lens catalogues, and we compute wavelet-based non-Gaussian statistics in the context of combined probes and their potential when applied to the weak-lensing convergence maps and galaxy maps. We obtain forecasts on the matter density parameter Ω m , the reduced Hubble constant h , the matter fluctuation amplitude σ 8 , and the dark energy equation of state parameter w 0 . In our setting for this first application, we consider the two probes to be independent. We find that the starlet peaks and the ℓ 1 -norm represent interesting summary statistics that can improve the constraints with respect to the power spectrum, even in the case of photometric galaxy clustering and when the two probes are combined.