A new method for the determination of the growth rate from galaxy redshift surveys

Given a redshift survey of galaxies with measurements of apparent magnitudes, we present a novel method for measuring the growth rate f(Ω) of cosmological linear perturbations. We use the galaxy distribution within the survey to solve for the peculiar velocity field which depends in linear perturbation theory on β = f(Ω)/b, where b is the bias factor of the galaxy distribution. The recovered line-of-sight peculiar velocities are subtracted from the redshifts to derive the distances, which thus allows an estimate of the absolute magnitude of each galaxy. A constraint on β is then found by minimizing the spread of the estimated magnitudes from their distribution function. We apply the method to the all sky K = 11.25 2MASS Redshift Survey and derive β = 0.35 0.1 at z 0, remarkably consistent with our previous estimate from the velocity-velocity comparison. The method could easily be applied to subvolumes extracted from the Sloan Digital Sky Survey to derive the growth rate at z 0.1. Further, it should also be applicable to ongoing and future spectroscopic redshift surveys to trace the evolution of f(Ω) to z 1. Constraints obtained from this method are entirely independent from those obtained from the two-dimensional distortion of ξ(s) and provide an important check on f(Ω), as alternative gravity models predict observable differences.