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 $f(\Omega)$ 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 $\beta=f(\Omega)/b$, 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 $\beta$ is then found by minimizing the spread of the estimated magnitudes from their distribution function. We apply the method to the all sky $K = 11.25$ Two-MASS Redhsift Survey (2MRS) and derive $\beta=0.35\pm 0.1$ at $z\sim 0$, remarkably consistent with our previous estimate from the velocity-velocity comparison. The method could easily be applied to subvolumes extracted from the SDSS survey to derive the growth rate at $z \sim 0.1$. Further, it should also be applicable to ongoing and future spectroscopic redshift surveys to trace the evolution of $f(\Omega)$ to $z\sim1$. Constraints obtained from this method are entirely independent from those obtained from the two-dimensional distortion of $\xi(s)$ and provide an important check on $f(\Omega)$, as alternative gravity models predict observable differences.