In this paper we explore the effect of decaying dark matter ( DDM ) on large-scale structure and possible constraints from galaxy imaging surveys .
DDM models have been studied , in part , as a way to address apparent discrepancies between the predictions of standard cold dark matter models and observations of galactic structure .
Our study is aimed at developing independent constraints on these models .
In such models , DDM decays into a less massive , stable dark matter ( SDM ) particle and a significantly lighter particle .
The small mass splitting between the parent DDM and the daughter SDM provides the SDM with a recoil or “ kick ” velocity v _ { k } , inducing a free-streaming suppression of matter fluctuations .
This suppression may be probed via weak lensing power spectra measured by a number of forthcoming imaging surveys that aim primarily to constrain dark energy .
Using scales on which linear perturbation theory alone is valid ( multipoles \ell < 300 ) , surveys like Euclid or LSST can be sensitive to v _ { k } \gtrsim 90 km/s for lifetimes \tau \sim 1 - 5 Gyr .
To estimate more aggressive constraints , we model nonlinear corrections to lensing power using a simple halo evolution model that is in good agreement with numerical simulations .
In our most ambitious forecasts , using multipoles \ell < 3000 , we find that imaging surveys can be sensitive to v _ { k } \sim 10 km/s for lifetimes \tau \lesssim 10 Gyr .
Lensing will provide a particularly interesting complement to existing constraints in that they will probe the long lifetime regime ( \tau \gg H _ { 0 } ^ { -1 } ) far better than contemporary techniques .
A caveat to these ambitious forecasts is that the evolution of perturbations on nonlinear scales will need to be well calibrated by numerical simulations before they can be realized .
This work motivates the pursuit of such a numerical simulation campaign to constrain dark matter with cosmological weak lensing .