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 $K = 11.25$ Two-MASS Redhsift Survey (2MRS) and derive $β=0.35\pm 0.1$ 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 $f(Ω)$ to $z\sim1$. 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.

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