Differentiating dark energy and modified gravity with galaxy redshift surveys

Abstract

The observed cosmic acceleration today could be due to an unknown energy component (dark energy), or a modification to general relativity (modified gravity). If dark energy models and modified gravity models are required to predict the same cosmic expansion history H(z), they will predict different growth 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). If gravity is not modified, the measured H(z) leads to a unique prediction for f_g(z), f_g^H(z). Comparing f_g^H(z) with the measured f_g(z) provides a transparent and straightforward test of gravity. We show that a simple \chi^2 test provides a general figure-of-merit for our ability to distinguish between dark energy and modified gravity given the measured H(z) and f_g(z). We study a magnitude-limited NIR galaxy redshift survey covering >10,000 (deg)^2 and the redshift range of 0.5<z<2. The resultant data can be divided into 7 redshift bins, and yield the measurement of H(z) to the accuracy of 1-2% via baryon acoustic oscillation measurements, and f_g(z) to the accuracy of a few percent via the measurement of redshift space distortions and the bias factor which describes how light traces mass. We find that if the H(z) data are fit by both a DGP gravity model and an equivalent dark energy model that predict the same expansion history, a survey area of 11,931 (deg)^2 is required to rule out the DGP gravity model at the 99.99% confidence level. It is feasible for such a galaxy redshift survey to be carried out by the next generation space missions from NASA and ESA, and it will revolutionize our understanding of the universe by differentiating between dark energy and modified gravity.