Differentiating dark energy and modified gravity with galaxy redshift surveys

The observed cosmic acceleration today could be due to an unknown energy component ( dark energy), or a modi. cation 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 rates for cosmic large scale structure, f(g)(z). If gravity is not modified, the measured H(z) leads to a unique prediction for f(g)( z), f(g)(H)(z), if dark energy and dark matter are separate. 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 fg(z). We find that a magnitude-limited NIR galaxy redshift survey covering > 10000(deg)(2) and a redshift range of 0.5 < z < 2 can be used to measure H(z) to 1 - 2% accuracy via baryon acoustic oscillation measurements, and f(g)(z) to the accuracy of a few per cent via the measurement of redshift-space distortions and the bias factor which describes how light traces mass. We show that if the H( z) data are fitted by both a DGP gravity model and an equivalent dark energy model that predict the same H(z), a survey area of 11931 (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.