Difficulties distinguishing dark energy from modified gravity via redshift distortions

The bulk motion of galaxies induced by the growth of cosmic structure offers a rare opportunity to test the validity of general relativity across cosmological scales. However, modified gravity can be degenerate in its effect with the unknown values of cosmological parameters. More seriously, even the “observed” value of the redshift-space distortions used to measure the fluctuation growth rate depends on the assumed cosmological parameters (the Alcock-Paczynski effect). We give a full analysis of these issues, showing how to combine redshift-space distortions with baryon acoustic oscillations and CMB data, in order to obtain joint constraints on deviations from general relativity and on the equation of state of dark energy while allowing for factors such as nonzero curvature. In particular we note that the evolution of Ωm(z), along with the Alcock-Paczynski effect, produces a degeneracy between the equation of state w and the modified growth parameter γ. Typically, the total marginalized error on either of these parameters will be larger by a factor ≃2 compared to the conditional error where one or the other is held fixed. We argue that future missions should be judged by their figure of merit as defined in the wp-γ plane, and note that the inclusion of spatial curvature can degrade this value by an order of magnitude.