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In this paper we explore the effect of decaying dark matter (DDM) onlarge-scale structure and possible constraints from galaxy imaging surveys. DDMmodels have been studied, in part, as a way to address apparent discrepanciesbetween the predictions of standard cold dark matter models and observations ofgalactic structure. Our study is aimed at developing independent constraints onthese models. In such models, DDM decays into a less massive, stable darkmatter (SDM) particle and a significantly lighter particle. The small masssplitting between the parent DDM and the daughter SDM provides the SDM with arecoil or "kick" velocity vk, inducing a free-streaming suppression of matterfluctuations. This suppression may be probed via weak lensing power spectrameasured by a number of forthcoming imaging surveys that aim primarily toconstrain dark energy. Using scales on which linear perturbation theory aloneis valid (multipoles < 300), surveys like Euclid or LSST can be sensitive to vk> 90 km/s for lifetimes ~ 1-5 Gyr. To estimate more aggressive constraints, wemodel nonlinear corrections to lensing power using a simple halo evolutionmodel that is in good agreement with numerical simulations. In our mostambitious forecasts, using multipoles < 3000, we find that imaging surveys canbe sensitive to vk ~ 10 km/s for lifetimes < 10 Gyr. Lensing will provide aparticularly interesting complement to existing constraints in that they willprobe the long lifetime regime far better than contemporary techniques. Acaveat to these ambitious forecasts is that the evolution of perturbations onnonlinear scales will need to be well calibrated by numerical simulationsbefore they can be realized. This work motivates the pursuit of such anumerical simulation campaign to constrain dark matter with cosmological weaklensing.

Effects of Unstable Dark Matter on Large-Scale Structure and Constraints from Future Surveys