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We consider the extent to which future imaging surveys of galaxies candistinguish between dark energy and modified gravity models for the origin ofthe cosmic acceleration. Dynamical dark energy models may have similarexpansion rates as models of modified gravity, yet predict different growth ofstructure histories. We parameterize the cosmic expansion by the twoparameters, $w_0$ and $w_a$, and the linear growth rate of density fluctuationsby Linder's $\gamma$, independently. Dark energy models generically predict$\gamma \approx 0.55$, while the DGP model $\gamma \approx 0.68$. To determineif future imaging surveys can constrain $\gamma$ within 20 percent (or$\Delta\gamma<0.1$), we perform the Fisher matrix analysis for a weak lensingsurvey such as the on-going Hyper Suprime-Cam (HSC) project. Under thecondition that the total observation time is fixed, we compute the Figure ofMerit (FoM) as a function of the exposure time $\texp$. We find that thetomography technique effectively improves the FoM, which has a broad peakaround $\texp\simeq {\rm several}\sim 10$ minutes; a shallow and wide survey ispreferred to constrain the $\gamma$ parameter. While $\Delta\gamma < 0.1$cannot be achieved by the HSC weak-lensing survey alone, one can improve theconstraints by combining with a follow-up spectroscopic survey like WFMOSand/or future CMB observations.

Optimizing future imaging survey of galaxies to confront dark energy and modified gravity models