The growth history of large-scale structure in the Universe is a powerful probe of the cosmological model, including the nature of dark energy. We study the growth rate of cosmic structure to redshift $z = 0.9$ using more than $162{,}000$ galaxy reds
hifts from the WiggleZ Dark Energy Survey. We divide the data into four redshift slices with effective redshifts $z = [0.2,0.4,0.6,0.76]$ and in each of the samples measure and model the 2-point galaxy correlation function in parallel and transverse directions to the line-of-sight. After simultaneously fitting for the galaxy bias factor we recover values for the cosmic growth rate which are consistent with our assumed $Lambda$CDM input cosmological model, with an accuracy of around 20% in each redshift slice. We investigate the sensitivity of our results to the details of the assumed model and the range of physical scales fitted, making close comparison with a set of N-body simulations for calibration. Our measurements are consistent with an independent power-spectrum analysis of a similar dataset, demonstrating that the results are not driven by systematic errors. We determine the pairwise velocity dispersion of the sample in a non-parametric manner, showing that it systematically increases with decreasing redshift, and investigate the Alcock-Paczynski effects of changing the assumed fiducial model on the results. Our techniques should prove useful for current and future galaxy surveys mapping the growth rate of structure using the 2-dimensional correlation function.
We use high-resolution N-body simulations to develop a new, flexible, empirical approach for measuring the growth rate from redshift-space distortions (RSD) in the 2-point galaxy correlation function. We quantify the systematic error in measuring the
growth rate in a $1 , h^{-3}$ Gpc$^3$ volume over a range of redshifts, from the dark matter particle distribution and a range of halo-mass catalogues with a number density comparable to the latest large-volume galaxy surveys such as the WiggleZ Dark Energy Survey and the Baryon Oscillation Spectroscopic Survey (BOSS). Our simulations allow us to span halo masses with bias factors ranging from unity (probed by emission-line galaxies) to more massive haloes hosting Luminous Red Galaxies. We show that the measured growth rate is sensitive to the model adopted for the small-scale real-space correlation function, and in particular that the standard assumption of a power-law correlation function can result in a significant systematic error in the growth rate determination. We introduce a new, empirical fitting function that produces results with a lower (5-10%) amplitude of systematic error. We also introduce a new technique which permits the galaxy pairwise velocity distribution, the quantity which drives the non-linear growth of structure, to be measured as a non-parametric stepwise function. Our (model-independent) results agree well with an exponential pairwise velocity distribution, expected from theoretical considerations, and are consistent with direct measurements of halo velocity differences from the parent catalogues. In a companion paper we present the application of our new methodology to the WiggleZ Survey dataset.
We place the most robust constraint to date on the scale of the turnover in the cosmological matter power spectrum using data from the WiggleZ Dark Energy Survey. We find this feature to lie at a scale of $k_0=0.0160^{+0.0041}_{-0.0035}$ [h/Mpc] (68%
confidence) for an effective redshift of 0.62 and obtain from this the first-ever turnover-derived distance and cosmology constraints: a measure of the cosmic distance-redshift relation in units of the horizon scale at the redshift of radiation-matter equality (r_H) of D_V(z=0.62)/r_H=18.3 (+6.3/-3.3) and, assuming a prior on the number of extra relativistic degrees of freedom $N_{eff}=3$, constraints on the matter density parameter $Omega_Mh^2=0.136^{+0.026}_{-0.052}$ and on the redshift of matter-radiation equality $z_{eq}=3274^{+631}_{-1260}$. All results are in excellent agreement with the predictions of standard LCDM models. Our constraints on the logarithmic slope of the power spectrum on scales larger than the turnover is bounded in the lower limit with values only as low as -1 allowed, with the prediction of standard LCDM models easily accommodated by our results. Lastly, we generate forecasts for the achievable precision of future surveys at constraining $k_0$, $Omega_Mh^2$, $z_{eq}$ and $N_{eff}$. We find that BOSS should substantially improve upon the WiggleZ turnover constraint, reaching a precision on $k_0$ of $pm$9% (68% confidence), translating to precisions on $Omega_Mh^2$ and $z_{eq}$ of $pm$10% (assuming a prior $N_{eff}=3$) and on $N_{eff}$ of (+78/-56)% (assuming a prior $Omega_Mh^2=0.135$). This is sufficient precision to sharpen the constraints on $N_{eff}$ from WMAP, particularly in its upper limit. For Euclid, we find corresponding attainable precisions on $(k_0, Omega_Mh^2, N_eff)$ of (3,4,+17/-21)%. This represents a precision approaching our forecasts for the Planck Surveyor.
