We present measurements of the baryon acoustic peak at redshifts z = 0.44, 0.6 and 0.73 in the galaxy correlation function of the final data set of the WiggleZ Dark Energy Survey. We combine our correlation function with lower redshift measurements from the 6-degree Field Galaxy Survey and Sloan Digital Sky Survey, producing a stacked survey correlation function in which the statistical significance of the detection of the baryon acoustic peak is 4.9σ relative to a zero-baryon model with no peak. We fit cosmological models to this combined baryon acoustic oscillation (BAO) data set comprising six distance-redshift data points, and compare the results with similar cosmological fits to the latest compilation of supernovae (SNe) and cosmic microwave background (CMB) data. The BAO and SNe data sets produce consistent measurements of the equation-of-state w of dark energy, when separately combined with the CMB, providing a powerful check for systematic errors in either of these distance probes. Combining all data sets we determine w = −1.03 ± 0.08 for a flat universe, consistent with a cosmological constant model. Assuming dark energy is a cosmological constant and varying the spatial curvature, we find k = −0.004 ± 0.006.

We perform a joint determination of the distance–redshift relation and cosmic expansion rate at redshifts z = 0.44, 0.6 and 0.73 by combining measurements of the baryon acoustic peak and Alcock–Paczynski distortion from galaxy clustering in the WiggleZ Dark Energy Survey, using a large ensemble of mock catalogues to calculate the covariance between the measurements. We find that DA(z) = (1205 ± 114, 1380 ± 95, 1534 ± 107) Mpc and H(z) = (82.6 ± 7.8, 87.9 ± 6.1, 97.3 ± 7.0) km s−1 Mpc−1 at these three redshifts. Further combining our results with other baryon acoustic oscillation and distant supernovae data sets, we use a Monte Carlo Markov Chain technique to determine the evolution of the Hubble parameter H(z) as a stepwise function in nine redshift bins of width Δz = 0.1, also marginalizing over the spatial curvature. Our measurements of H(z), which have precision better than 7 per cent in most redshift bins, are consistent with the expansion history predicted by a cosmological constant dark energy model, in which the expansion rate accelerates at redshift z < 0.7.

We present precise measurements of the growth rate of cosmic structure for the redshift range 0.1 < z < 0.9, using redshift‐space distortions in the galaxy power spectrum of the WiggleZ Dark Energy Survey. Our results, which have a precision of around 10 per cent in four independent redshift bins, are well fitted by a flat Λ cold dark matter (ΛCDM) cosmological model with matter density parameter Ωm= 0.27. Our analysis hence indicates that this model provides a self‐consistent description of the growth of cosmic structure through large‐scale perturbations and the homogeneous cosmic expansion mapped by supernovae and baryon acoustic oscillations. We achieve robust results by systematically comparing our data with several different models of the quasi‐linear growth of structure including empirical models, fitting formulae calibrated to N‐body simulations, and perturbation theory techniques. We extract the first measurements of the power spectrum of the velocity divergence field, Pθθ(k), as a function of redshift (under the assumption that , where g is the galaxy overdensity field), and demonstrate that the WiggleZ galaxy–mass cross‐correlation is consistent with a deterministic (rather than stochastic) scale‐independent bias model for WiggleZ galaxies for scales k < 0.3 h Mpc−1. Measurements of the cosmic growth rate from the WiggleZ Survey and other current and future observations offer a powerful test of the physical nature of dark energy that is complementary to distance–redshift measures such as supernovae and baryon acoustic oscillations.

The WiggleZ Dark Energy Survey is a survey of 240 000 emission‐line galaxies in the distant Universe, measured with the AAOmega spectrograph on the 3.9‐m Anglo‐Australian Telescope (AAT). The primary aim of the survey is to precisely measure the scale of baryon acoustic oscillations (BAO) imprinted on the spatial distribution of these galaxies at look‐back times of 4–8 Gyr. The target galaxies are selected using ultraviolet (UV) photometry from the Galaxy Evolution Explorer satellite, with a flux limit of NUV < 22.8 mag. We also require that the targets are detected at optical wavelengths, specifically in the range 20.0 < r < 22.5 mag. We use the Lyman break method applied to the UV colours, with additional optical colour limits, to select high‐redshift galaxies. The galaxies generally have strong emission lines, permitting reliable redshift measurements in relatively short exposure times on the AAT. The median redshift of the galaxies is zmed= 0.6. The redshift range containing 90 per cent of the galaxies is 0.2 < z < 1.0. The survey will sample a volume of ∼1 Gpc3 over a projected area on the sky of 1000 deg2, with an average target density of 350 deg−2. Detailed forecasts indicate that the survey will measure the BAO scale to better than 2 per cent and the tangential and radial acoustic wave scales to approximately 3 and 5 per cent, respectively. Combining the WiggleZ constraints with existing cosmic microwave background measurements and the latest supernova data, the marginalized uncertainties in the cosmological model are expected to be σ(Ωm) = 0.02 and σ(w) = 0.07 (for a constant w model). The WiggleZ measurement of w will constitute a robust, precise and independent test of dark energy models. This paper provides a detailed description of the survey and its design, as well as the spectroscopic observations, data reduction and redshift measurement techniques employed. It also presents an analysis of the properties of the target galaxies, including emission‐line diagnostics which show that they are mostly extreme starburst galaxies, and Hubble Space Telescope images, which show that they contain a high fraction of interacting or distorted systems. In conjunction with this paper, we make a public data release of data for the first 100 000 galaxies measured for the project.

We present significant improvements in cosmic distance measurements from the Wig-gleZ Dark Energy Survey, achieved by applying the reconstruction of the baryonic acoustic feature technique. We show using both data and simulations that the reconstruction technique can often be effective despite patchiness of the survey, significant edge effects and shot-noise. We investigate three redshift bins in the redshift range 0.2 < z < 1, and in all three find improvement after reconstruction in the detection of the baryonic acoustic feature and its usage as a standard ruler. We measure model independent distance measures D V r fid s /r s of 1716± 83 Mpc, 2221± 101 Mpc, 2516± 86 Mpc (68% CL) at effective redshifts z = 0.44, 0.6, 0.73, respectively, where D V is the volume-average-distance, and r s is the sound horizon at the end of the baryon drag epoch. These significantly improved 4.8, 4.5 and 3.4 per-cent accuracy measurements are equivalent to those expected from surveys with up to 2.5 times the volume of WiggleZ without reconstruction applied. These measurements are fully consistent with cosmologies allowed by the analyses of the Planck Collaboration and the Sloan Digital Sky Survey. We provide the D V r fid s /r s posterior probability distributions and their covariances. When combining these measurements with temperature fluctuations measurements of Planck, the polarization of WMAP9, and the 6dF Galaxy Survey baryonic acoustic feature, we do not detect deviations from a flat ΛCDM model. Assuming this model we constrain the current expansion rate to H 0 = 67.15 ± 0.98 kms −1 Mpc −1 . Allowing the equation of state of dark energy to vary we obtain w DE = −1.080 ± 0.135. When assuming a curved ΛCDM model we obtain a curvature value of Ω K = −0.0043 ± 0.0047. c 0000 RAS 2 Kazin E., Koda J., Blake C. et al.

The influence of a galaxy’s environment on its evolution has been studied and compared extensively in the literature, although differing techniques are often used to define environment. Most methods fall into two broad groups: those that use nearest neighbours to probe the underlying density field and those that use fixed apertures. The differences between the two inhibit a clean comparison between analyses and leave open the possibility that, even with the same data, different properties are actually being measured. In this work, we apply 20 published environment definitions to a common mock galaxy catalogue constrained to look like the local Universe. We find that nearest‐neighbour‐based measures best probe the internal densities of high‐mass haloes, while at low masses the interhalo separation dominates and acts to smooth out local density variations. The resulting correlation also shows that nearest‐neighbour galaxy environment is largely independent of dark matter halo mass. Conversely, aperture‐based methods that probe superhalo scales accurately identify high‐density regions corresponding to high‐mass haloes. Both methods show how galaxies in dense environments tend to be redder, with the exception of the largest apertures, but these are the strongest at recovering the background dark matter environment. We also warn against using photometric redshifts to define environment in all but the densest regions. When considering environment, there are two regimes: the ‘local environment’ internal to a halo best measured with nearest neighbour and ‘large‐scale environment’ external to a halo best measured with apertures. This leads to the conclusion that there is no universal environment measure and the most suitable method depends on the scale being probed.

We measure the imprint of baryon acoustic oscillations (BAOs) in the galaxy clustering pattern at the highest redshift achieved to date, z= 0.6, using the distribution of N= 132 509 emission‐line galaxies in the WiggleZ Dark Energy Survey. We quantify BAOs using three statistics: the galaxy correlation function, power spectrum and the band‐filtered estimator introduced by Xu et al. The results are mutually consistent, corresponding to a 4.0 per cent measurement of the cosmic distance–redshift relation at z= 0.6 [in terms of the acoustic parameter ‘A(z)’ introduced by Eisenstein et al., we find A(z= 0.6) = 0.452 ± 0.018]. Both BAOs and power spectrum shape information contribute towards these constraints. The statistical significance of the detection of the acoustic peak in the correlation function, relative to a wiggle‐free model, is 3.2σ. The ratios of our distance measurements to those obtained using BAOs in the distribution of luminous red galaxies at redshifts z= 0.2 and 0.35 are consistent with a flat Λ cold dark matter model that also provides a good fit to the pattern of observed fluctuations in the cosmic microwave background radiation. The addition of the current WiggleZ data results in a ≈30 per cent improvement in the measurement accuracy of a constant equation of state, w, using BAO data alone. Based solely on geometric BAO distance ratios, accelerating expansion (w < −1/3) is required with a probability of 99.8 per cent, providing a consistency check of conclusions based on supernovae observations. Further improvements in cosmological constraints will result when the WiggleZ survey data set is complete.

We have made the largest volume measurement to date of the transition to large‐scale homogeneity in the distribution of galaxies. We use the WiggleZ survey, a spectroscopic survey of over 200 000 blue galaxies in a cosmic volume of ∼1 h−3 Gpc3. A new method of defining the ‘homogeneity scale' is presented, which is more robust than methods previously used in the literature, and which can be easily compared between different surveys. Due to the large cosmic depth of WiggleZ (up to z = 1), we are able to make the first measurement of the transition to homogeneity over a range of cosmic epochs. The mean number of galaxies N(< r) in spheres of comoving radius r is proportional to r3 within 1 per cent, or equivalently the fractal dimension of the sample is within 1 per cent of D2 = 3, at radii larger than 71 ± 8 h−1Mpc at z ∼ 0.2, 70 ± 5 h−1 Mpc at z ∼ 0.4, 81 ± 5 h−1 Mpc at z ∼ 0.6 and 75 ± 4 h−1 Mpc at z ∼ 0.8. We demonstrate the robustness of our results against selection function effects, using a Λ cold dark matter (ΛCDM) N‐body simulation and a suite of inhomogeneous fractal distributions. The results are in excellent agreement with both the ΛCDM N‐body simulation and an analytical ΛCDM prediction. We can exclude a fractal distribution with fractal dimension below D2 = 2.97 on scales from ∼80 h−1 Mpc up to the largest scales probed by our measurement, ∼300 h−1 Mpc, at 99.99 per cent confidence.