Abstract
We present a new summary statistic for weak lensing observables, higher than second order, suitable for extracting non-Gaussian cosmological information and inferring cosmological parameters. We name this statistic the ‘starletℓ1-norm’ as it is computed via the sum of the absolute values of the starlet (wavelet) decomposition coefficients of a weak lensing map. In comparison to the state-of-the-art higher-order statistics – weak lensing peak counts and minimum counts, or the combination of the two – theℓ1-norm provides a fast multi-scale calculation of the full void and peak distribution, avoiding the problem of defining what a peak is and what a void is: theℓ1-norm carries the information encoded in all pixels of the map, not just the ones in local maxima and minima. We show its potential by applying it to the weak lensing convergence maps provided by theMassiveNussimulations to get constraints on the sum of neutrino masses, the matter density parameter, and the amplitude of the primordial power spectrum. We find that, in an ideal setting without further systematics, the starletℓ1-norm remarkably outperforms commonly used summary statistics, such as the power spectrum or the combination of peak and void counts, in terms of constraining power, representing a promising new unified framework to simultaneously account for the information encoded in peak counts and voids. We find that the starletℓ1-norm outperforms the power spectrum by 72% onMν, 60% on Ωm, and 75% onAsfor theEuclid-like setting considered; it also improves upon the state-of-the-art combination of peaks and voids for a single smoothing scale by 24% onMν, 50% on Ωm, and 24% onAs.
Highlights
Weak gravitational lensing by the large-scale structure represents a powerful tool for estimating cosmological parameters
It has been shown that this statistic is powerful in breaking degeneracy between the standard model and fifth forces in the dark sector (Peel et al 2018) as well as in constraining cosmological parameters when employed in a multi-scale setting (Liu et al 2015; Lin et al 2016; Fluri et al 2018b; Ajani et al 2020; Zürcher et al 2020)
Ajani et al (2020) have shown that multi-scale peak counts significantly outperform the weak lensing power spectrum, improving the constraints on the sum of neutrino masses mν ≡ Mν by 63% when using a starlet filter; multi-scale peak counts were shown to be so constraining that the addition of the power spectrum does not further improve constraints
Summary
Weak gravitational lensing by the large-scale structure represents a powerful tool for estimating cosmological parameters. A very interesting feature of multiscale peaks, when they are obtained using the starlet transform (Starck et al 2007), is the behaviour of the covariance matrix that tends to encode all information in its diagonal elements Another weak lensing probe of large-scale structure is represented by cosmic voids, namely under-dense regions of the large-scale matter field (Colberg et al 2008; Pisani et al 2019). In this Letter, we propose, for the first time, using the 1norm of wavelet coefficients of weak lensing convergence maps We show that it provides a unified framework for a joint multiscale peak and void analysis and that it takes into account the information encoded in all pixels of the map.
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