![]() Measurements for the growth at different environment can thus be used as a test for departures from Einstein gravity. But the environmental dependence of the growth of structure may have a more fundamental significance, since it could encode information about non-standard theories of gravity. ![]() The scales where such nonlinear growth effects become important will probably differ between different environments. At a minimum, the growth of density perturbations is expected to be more rapid in superclusters and lower in voids, simply because these regions resemble universes with different cosmological parameters. This average growth is extracted from the pairwise galaxy–galaxy correlations, which sample peaks and troughs of the matter density field it remains an open question, at least from the observational point of view, how the growth of structure depends on the environment. 2016) with care, it is possible to recover the linear growth rate to 2 per cent precision by including this small-scale information (Reid et al. 2011 Seljak & McDonald 2011 de la Torre & Guzzo 2012 Gil-Marín et al. Scoccimarro 2004 Matsubara 2008 Percival & White 2009 Taruya et al. The pairwise galaxy–galaxy power spectrum or correlation function approaches the prediction of linear theory at very large scales, but in the quasi-linear and nonlinear regime, more sophisticated models are needed to account for nonlinear growth (e.g. Using redshift-space distortions (RSDs) to probe the growth of large-scale structure has been a target for cosmological research since the first prediction of the effect (Kaiser 1987) and observational RSD studies have been pursued for over two decades (e.g. Methods: analytical, methods: numerical, methods: statistical, large-scale structure of Universe 1 INTRODUCTION This diversity of redshift-space void morphology complicates measurements of the Alcock–Paczynski effect using voids. The distortion pattern is therefore determined solely by the void profile and is different for void-in-cloud and void-in-void. This can be explained by the competing amplitudes of the local density contrast, plus the radial velocity profile and its gradient. Voids show diverse shapes in redshift space, and can appear either elongated or flattened along the line of sight. The precision on β is reduced to 5 per cent. Adding velocity dispersion as a free parameter allows us to use information at radii as small as half of the void radius. Smaller voids are predominantly sub-voids, which may be more sensitive to the random velocity dispersion they introduce noise and do not help to improve measurements. We recover the linear growth parameter β to 9 per cent precision from an effective volume of 3( h −1Gpc) 3 using voids with radius >25 h −1Mpc. By extracting the monopole and quadrupole from the CCF, we measure the linear growth rate without prior knowledge of the void profile or velocity dispersion. At scales greater than the void radius, linear theory is a good match to voids traced out by haloes small-scale random velocities are unimportant at these radii, only tending to cause small and often negligible elongation of the CCF near its origin. In linear theory, this CCF contains only monopole and quadrupole terms. We have derived estimators for the linear growth rate of density fluctuations using the cross-correlation function (CCF) of voids and haloes in redshift space.
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