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.