Constraining neutrino mass with the tomographic weak lensing bispectrum

We explore the effect of massive neutrinos on the weak lensing shear bispectrum using the Cosmological Massive Neutrino Simulations [1]. We find that the primary effect of massive neutrinos is to suppress the amplitude of the bispectrum with limited effect on the bispectrum shape. The suppression of the bispectrum amplitude is a factor of two greater than the suppression of the small scale power-spectrum. For an LSST-like weak lensing survey that observes half of the sky with five tomographic redshift bins, we explore the constraining power of the bispectrum on three cosmological parameters: the sum of the neutrino mass ∑ m_ν, the matter density Ω_m and the amplitude of primordial fluctuations A_s. Bispectrum measurements alone provide similar constraints to the power spectrum measurements and combining the two probes leads to significant improvements than using the latter alone. We find that the joint constraints tighten the power spectrum 95% constraints by ∼ 32% for ∑ m_ν, 13% for Ω_m and 57% for A_s.