Constraining neutrino masses with weak-lensing starlet peak counts

Massive neutrinos influence the background evolution of the Universe as well as the growth of structure. Being able to model this effect and constrain the sum of their masses is one of the key challenges in modern cosmology. Weak gravitational lensing by the large-scale structure has proven to be a powerful tool to achieve this goal, and its importance to precision cosmology is borne out in the scientific results of galaxy surveys such as the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS), the Kilo-Degree Survey (KiDS), the Dark Energy Survey (DES) and Hyper SuprimeCam (HSC). Weak-lensing cosmological constraints will also soon reach higher levels of precision with next-generation surveys like LSST, WFIRST and Euclid. In this context, we use the MassiveNus simulations to derive constraints on the sum of neutrino masses $M_{\nu}$, the present-day total matter density ${\Omega}_m$, and the primordial power spectrum normalization $A_s$ in a tomographic setting. Along with the lensing power spectrum, we use peak counts as higher-order statistics. We find that the combination of the two statistics does not add any relevant information over considering just the peaks alone. We also compare two different filtering techniques on noisy maps and show that a starlet (wavelet) filter produces tighter constraints than Gaussian filtering by 50%, 25%, and 38% on $M_{\nu}$, ${\Omega}_m$, and $A_s$, respectively. For the starlet case, we further find a minimum resolution that allows us to obtain constraints comparable to what is achieved with the full wavelet decomposition, and we show that the information contained in the coarse map cannot be neglected.