  The nature of the dark matter remains a mystery. The possibility of an
unstable dark matter particle decaying to invisible daughter particles has been
explored many times in the past few decades. Meanwhile, weak gravitational
lensing shear has gained a lot of attention as a probe of dark energy. Weak
lensing is a useful tool for constraining the stability of the dark matter. In
the coming decade a number of large, galaxy imaging surveys will be undertaken
and will measure the statistics of cosmological weak lensing with unprecedented
precision. Weak lensing statistics are sensitive to unstable dark matter in at
least two ways. Dark matter decays alter the matter power spectrum and change
the angular diameter distance-redshift relation. We show how measurements of
weak lensing shear correlations may provide the most restrictive,
model-independent constraints on the lifetime of unstable dark matter. Our
results rely on assumptions regarding nonlinear evolution of density
fluctuations in scenarios of unstable dark matter and one of our aims is to
stimulate interest in theoretical work on nonlinear structure growth in
unstable dark matter models.
