3D weak lensing: Modified theories of gravity

Weak lensing (WL) promises to be a particularly sensitive probe of both the growth of large-scale structure as well as the fundamental relation between matter density perturbations and metric perturbations, thus providing a powerful tool with which we may constrain modified theories of gravity (MG) on cosmological scales. Future deep, wide-field WL surveys will provide an unprecedented opportunity to constrain deviations from General Relativity. Employing a 3D analysis based on the spherical FourierBessel expansion, we investigate the extent to which MG theories will be constrained by a typical 3D WL survey configuration including noise from the intrinsic ellipticity distribution σε of source galaxies. Here, we focus on two classes of screened theories of gravity: (i) fðRÞ chameleon models and (ii) environmentally dependent dilaton models. We use one-loop perturbation theory combined with halo models in order to accurately model the evolution of the matter power spectrum with redshift in these theories. Using a χ analysis, we show that for an all-sky spectroscopic survey, the parameter fR0 can be constrained in the range fR0 < 5 × 10 −6ð9 × 10−6Þ for n 1⁄4 1ð2Þ with a 3σ confidence level. This can be achieved by using relatively low-order angular harmonics l < 100. Higher-order harmonics l > 100 could provide tighter constraints but are subject to nonlinear effects, such as baryonic feedback, that must be accounted for. We also employ a Principal Component Analysis in order to study the parameter degeneracies in the MG parameters. The confusion from intrinsic ellipticity correlation and modification of the matter power spectrum at a small scale due to feedback mechanisms is briefly discussed.