Reconstructing the history of structure formation using redshift distortions

Measuring the statistics of galaxy peculiar velocities using redshift-space distortions is an excellent way of probing the history of structure formation. Because galaxies are expected to act as test particles within the flow of matter, this method avoids uncertainties due to an unknown galaxy density bias. We show that the parameter combination measured by redshift-space distortions, $f\sigma_8^{\rm mass}$ provides a good test of dark energy models, even without the knowledge of bias or $\sigma_8^{\rm mass}$ required to extract $f$ from this measurement (here $f$ is the logarithmic derivative of the linear growth rate, and $\sigma_8^{\rm mass}$ is the root-mean-square mass fluctuation in spheres with radius $8h^{-1}$Mpc). We argue that redshift-space distortion measurements will help to determine the physics behind the cosmic acceleration, testing whether it is related to dark energy or modified gravity, and will provide an opportunity to test possible dark energy clumping or coupling between dark energy and dark matter. If we can measure galaxy bias in addition, simultaneous measurement of both the overdensity and velocity fields can be used to test the validity of equivalence principle, through the continuity equation.