The WiggleZ Dark Energy Survey: the growth rate of cosmic structure since redshift z=0.9

TL;DR

This study delivers precise measurements of the growth rate of cosmic structure in the intermediate redshift universe (0.1 < z < 0.9) using redshift-space distortions in the WiggleZ galaxy power spectrum. By evaluating a suite of 18 quasi-linear models—ranging from empirical damping to perturbation theory and N-body-calibrated fits—the authors extract f and the galaxy bias b, demonstrating consistency with a flat ΛCDM cosmology (Ω_m = 0.27) and General Relativity. They additionally measure the cross-correlation between galaxies and matter, finding the bias to be effectively deterministic (r ≈ 1) on scales k < 0.3 h/Mpc, and they present the first measurements of the velocity divergence power spectrum P_θθ(z). The work reinforces growth-rate measurements as a complementary probe of dark energy and gravity, alongside distance indicators, and sets the stage for joint analyses with Alcock-Paczynski tests and CMB data.

Abstract

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% in four independent redshift bins, are well-fit by a flat LCDM cosmological model with matter density parameter Omega_m = 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, P_vv(k), as a function of redshift (under the assumption that P_gv(k) = -sqrt[P_gg(k) P_vv(k)] 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. 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.

Figures (11)

• Figure 1: Greyscale map illustrating the relative redshift completeness of each of the six WiggleZ survey regions analyzed in this paper. This Figure is generated by taking the ratio of the galaxy densities in the redshift and parent catalogues in small cells. The $x$-axis and $y$-axis of each panel represent right ascension and declination, respectively.
• Figure 2: The galaxy power spectrum amplitude as a function of wavevectors $(k_\perp,k_\parallel)$ perpendicular and parallel to the line-of-sight, determined by stacking observations in different WiggleZ survey regions in four redshift slices. The contours correspond to the best-fitting non-linear empirical Lorentzian redshift-space distortion model. We note that because of the differing degrees of convolution in each region due to the window function, a "de-convolution" method was used to produce this plot. Before stacking, the data points were corrected by the ratio of the unconvolved and convolved two-dimensional power spectra corresponding to the best-fitting model, for the purposes of this visualization. Only the top-right quadrant of data for each redshift is independent; the other three quadrants are mirrors of this first quadrant. The $k_\perp = 0$ axis is noisiest because it contains the lowest number of Fourier modes available for power spectrum determination.
• Figure 3: The galaxy power spectrum as a function of amplitude and angle of Fourier wavevector $(k,\mu)$, determined by stacking observations in different WiggleZ survey regions in four redshift slices. The contours correspond to the best-fitting non-linear empirical Lorentzian redshift-space distortion model. A similar stacking method was used to that employed in the generation of Figure \ref{['figpkcomp']}. In the absence of redshift-space distortions, the model contours would be horizontal lines.
• Figure 4: The multipole power spectra $P_\ell(k)$ for $\ell=0,2,4$ for the different models listed in Table \ref{['tabmodlist']}. The models are evaluated at redshift $z=0.6$ assuming a linear bias $b=1$, a growth rate $f=0.7$ and (where applicable) a damping term $\sigma_v = 300 \, h$ km s$^{-1}$. The models are labelled by their row number in Table \ref{['tabmodlist']}. The solid and dashed lines are models that respectively include and exclude the damping term. All models are divided by a smooth "no-wiggles" reference power spectrum from the fitting formulae of Eisenstein & Hu (1998), which has the same shape as the linear power spectrum but without the imprint of baryon acoustic oscillations. The models agree well in the large-scale limit, but significant differences develop between the models at smaller scales.
• Figure 5: Measurements of the growth rate $f$ for the $0.5 < z < 0.7$ redshift slice for each of the 18 models listed in Table \ref{['tabmodlist']}. The three panels, each consisting of a pair of plots, correspond to different ranges of fitted scales $0 < k < k_{\rm max}$ where $k_{\rm max} = 0.1, 0.2$ and $0.3 \, h$ Mpc$^{-1}$. For each panel the left-hand plot shows the measurement of $f$ and the right-hand plot displays the minimum value of the $\chi^2$ statistic relative to the best-fitting model for that choice of $k_{\rm max}$. In the left-hand plot, the vertical dashed line indicates the prediction of a flat $\Lambda$CDM cosmological model with $\Omega_{\rm m} = 0.27$. The two vertical dotted lines span the $68\%$ confidence region of the growth rate measured for the Jennings et al. model with a variable damping parameter, facilitating an easy comparison of the results for different models. In the right-hand plot, points with $\Delta \chi^2 < 0.1$ are plotted at the left-hand edge of the panel and $\Delta \chi^2 = 1$ is indicated by the vertical dashed line. The three best-performing models for $k_{\rm max} = 0.3$ are highlighted by red text.