Optimal Weak Lensing Skewness Measurements

Weak lensing measurements are starting to provide statistical maps of the distribution of matter in the universe that are increasingly precise and complementary to cosmic microwave background maps. The most common measurement is the correlation in alignments of background galaxies which can be used to infer the variance of the projected surface density of matter. This measurement of the fluctuations is insensitive to the total mass content and is analogous to using waves on the ocean to measure its depths. However, when the depth is shallow as happens near a beach waves become skewed. Similarly, a measurement of skewness in the projected matter distribution directly measures the total matter content of the universe. While skewness has already been convincingly detected, its constraint on cosmology is still weak. We address optimal analyses for the CFHT Legacy Survey in the presence of noise. We show that a compensated Gaussian filter with a width of 2.5 arc minutes optimizes the cosmological constraint, yielding ∆Ωm/Ωm ∼ 10%. This is significantly better than other filters which have been considered in the literature. This can be further improved with tomography and other sophisticated analyses.