The growth rate of cosmic structure from peculiar velocities at low and high redshifts

Peculiar velocities are an important probe of the growth rate of mass density fluctuations in the Universe. Most previous studies have focussed exclusively on measuring peculiar velocities at intermediate ($0.2 < z < 1$) redshifts using statistical redshift-space distortions. Here we emphasize the power of peculiar velocities obtained directly from distance measurements at low redshift ($z \lesssim 0.05$), and show that these data break the usual degeneracies in the \Omega_{m,0} -- $\sigma_{8,0}$ parameter space. Using only peculiar velocity data, we find $\Omega_{m,0} = 0.259\pm0.045$ and $\sigma_{8,0} = 0.748\pm0.035$. Fixing the amplitude of fluctuations at very high redshift using observations of the Cosmic Microwave Background (CMB), the same data can be used to constrain the growth index $\gamma$, with the strongest constraints coming from peculiar velocity measurements in the nearby Universe. We find $\gamma = 0.619\pm 0.054$, consistent with LCDM. Current peculiar velocity data already strongly constrain modified gravity models, and will be a powerful test as data accumulate.