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.

We present the properties of eight star‐forming regions, or ‘clumps,’ in three galaxies at z∼ 1.3 from the WiggleZ Dark Energy Survey, which are resolved with the OH Suppressing InfraRed Imaging Spectrograph (OSIRIS) integral field spectrograph. Within turbulent discs, σ∼ 90 km s−1, clumps are measured with average sizes of 1.5 kpc and average Jeans masses of 4.2 × 109 M⊙, in total accounting for 40–60 per cent of the stellar mass of the discs. These findings lend observational support to models that predict larger clumps will form as a result of higher disc velocity dispersions driven‐up by cosmological gas accretion. As a consequence of the changes in global environment, it may be predicted that star‐forming regions at high redshift should not resemble star‐forming regions locally. Yet despite the increased sizes and dispersions, clumps and H ii regions are found to follow tight scaling relations over the range z= 0–2 for Hα size, velocity dispersion, luminosity and mass when comparing >2000 H ii regions locally and 30 clumps at z > 1 (σ∝r0.42 ± 0.03, LHα∝r2.72 ± 0.04, LHα∝σ4.18 ± 0.21 and ). We discuss these results in the context of the existing simulations of clump formation and evolution, with an emphasis on the processes that drive‐up the turbulent motions in the interstellar medium. Our results indicate that while the turbulence of discs may have important implications for the size and luminosity of regions which form within them, the same processes govern their formation from high redshift to the current epoch.

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.