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The nature of the dark matter remains a mystery. The possibility of anunstable dark matter particle decaying to invisible daughter particles has beenexplored many times in the past few decades. Meanwhile, weak gravitationallensing shear has gained a lot of attention as a probe of dark energy. Weaklensing is a useful tool for constraining the stability of the dark matter. Inthe coming decade a number of large, galaxy imaging surveys will be undertakenand will measure the statistics of cosmological weak lensing with unprecedentedprecision. Weak lensing statistics are sensitive to unstable dark matter in atleast two ways. Dark matter decays alter the matter power spectrum and changethe angular diameter distance-redshift relation. We show how measurements ofweak lensing shear correlations may provide the most restrictive,model-independent constraints on the lifetime of unstable dark matter. Ourresults rely on assumptions regarding nonlinear evolution of densityfluctuations in scenarios of unstable dark matter and one of our aims is tostimulate interest in theoretical work on nonlinear structure growth inunstable dark matter models.

Weak Gravitational Lensing as a Method to Constrain Unstable Dark Matter