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The observed cosmic acceleration today could be due to an unknown energycomponent (dark energy), or a modification to general relativity (modifiedgravity). If dark energy models and modified gravity models are required topredict the same cosmic expansion history H(z), they will predict differentgrowth rate for cosmic large scale structure, f_g(z)=d\ln \delta/d\ln a(\delta=(\rho_m-\bar{\rho_m})/\bar{\rho_m}), a is the cosmic scale factor). Ifgravity is not modified, the measured H(z) leads to a unique prediction forf_g(z), f_g^H(z). Comparing f_g^H(z) with the measured f_g(z) provides atransparent and straightforward test of gravity. We show that a simple \chi^2test provides a general figure-of-merit for our ability to distinguish betweendark energy and modified gravity given the measured H(z) and f_g(z). We study amagnitude-limited NIR galaxy redshift survey covering >10,000 (deg)^2 and theredshift range of 0.5<z<2. The resultant data can be divided into 7 redshiftbins, and yield the measurement of H(z) to the accuracy of 1-2% via baryonacoustic oscillation measurements, and f_g(z) to the accuracy of a few percentvia the measurement of redshift space distortions and the bias factor whichdescribes how light traces mass. We find that if the H(z) data are fit by botha DGP gravity model and an equivalent dark energy model that predict the sameexpansion history, a survey area of 11,931 (deg)^2 is required to rule out theDGP gravity model at the 99.99% confidence level. It is feasible for such agalaxy redshift survey to be carried out by the next generation space missionsfrom NASA and ESA, and it will revolutionize our understanding of the universeby differentiating between dark energy and modified gravity.

Differentiating dark energy and modified gravity with galaxy redshift surveys