Optimal Weak‐Lensing Skewness Measurements

Weak lensing measurements are entering a precision era to statistically mapthe distribution of matter in the universe. The most common measurement hasbeen of the variance of the projected surface density of matter, whichcorresponds to the induced correlation in alignments of background galaxies.This measurement of the fluctuations is insensitive to the total mass content,like using waves on the ocean to measure its depths. But when the depth isshallow as happens near a beach, waves become skewed. Similarly, a measurementof skewness in the projected matter distribution directly measures the totalmatter content of the universe. While skewness has already been convincinglydetected, its constraint on cosmology is still weak. We address optimalanalyses for the CFHT Legacy Survey in the presence of noise. We show that acompensated Gaussian filter with a width of 2.5 arc minutes optimizes thecosmological constraint, yielding $\Delta \Omega_m/\Omega_m\sim 10%$. This issignificantly better than other filters which have been considered in theliterature. This can be further improved with tomography and othersophisticated analyses.Comment: 19 pages including 6 figures and 1 table, accepted for publication in ApJ, minor revision