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Weak lensing (WL) promises to be a particularly sensitive probe of both thegrowth of large scale structure (LSS) as well as the fundamental relationbetween matter density perturbations and metric perturbations, thus providing apowerful tool with which we may constrain modified theories of gravity (MG) oncosmological scales. Future deep, wide-field WL surveys will provide anunprecedented opportunity to constrain deviations from General Relativity (GR).Employing a three-dimensional (3D) analysis based on the sphericalFourier-Bessel (sFB) expansion, we investigate the extent to which MG theorieswill be constrained by a typical 3D WL survey configuration including noisefrom the intrinsic ellipticity distribution $\sigma_{\epsilon}$ of sourcegalaxies. Here we focus on two classes of screened theories of gravity: i)$f(R)$ chameleon models and ii) environmentally dependent dilaton models. Weuse one-loop perturbation theory combined with halo models in order toaccurately model the evolution of matter power-spectrum with redshift in thesetheories. Using a Fisher information matrix based approach, we show that for anall-sky spectroscopic survey, the parameter $f_{R_0}$ can be constrained in therange $f_{R_0}< 5\times 10^{-6}(9\times 10^{-6})$ for $n=1(2)$ with a 3$\sigma$confidence level. This can be achieved by using relatively low order angularharmonics $\ell<100$. Including higher order harmonics $\ell>100$ can furthertighten the constraints, making them comparable to current solar-systemconstraints. We also employ a Principal Component Analysis (PCA) in order tostudy the parameter degeneracies in the MG parameters. Our results cantrivially be extended to other MG theories, such as the K-mouflage models. Theconfusion from intrinsic ellipticity correlation and modification of the matterpower-spectrum at small scale due to feedback mechanisms is briefly discussed.

3D Weak Lensing: Modified Theories of Gravity