Constraining Neutrino Mass with the Void Weak Lensing Effect

Cosmic voids, the underdense regions of the Large Scale Structure (LSS), provide cosmological information highly complementary to that obtained from overdense regions. In this work, we investigate the constraining power of the void-shear cross-correlation (void lensing effect) on the total neutrino mass. Based on cosmological $N$-body simulations with varying neutrino masses, we populate BOSS LOW-Z-like galaxies at $0.2<z<0.4$ using HOD fitting, identify voids with the DIVE void finder and obtain their density profiles from the underlying dark matter and neutrino distributions. We then generate mock shear catalogues through ray-tracing and measure the corresponding void lensing signals, assuming a source number density of $10/{\rm arcmin}^{2}$ and sky area of around $8400\,{\rm deg}^2$. Under this setup, void lensing independently yields a constraint on total neutrino mass as $\sigma(M_{\nu})=0.096\,{\rm eV}$ ($M_{\nu}<0.232\,{\rm eV}$, 95% C.L.) in the absence of shape noise, and $\sigma(M_{\nu})=0.340\,{\rm eV}$ ($M_{\nu}<0.707\,{\rm eV}$, 95% C.L.) when adopting a Stage-III-like shape noise. Moreover, we find a clear linear relationship between the void lensing signal and neutrino mass. We further validate the forward modelling of the void lensing signal from the void density profiles across different cosmologies, demonstrating its accuracy and potential for future applications. These findings highlight void lensing as a promising probe of massive neutrinos and motivate its applications to galaxy survey data as well as the combination with other cosmological observables.