The WiggleZ Dark Energy Survey: Final data release and cosmological results

This paper presents cosmological results from the final data release of the WiggleZ Dark Energy Survey. We perform full analyses of different cosmological models using the WiggleZ power spectra measured at $z=0.22$, 0.41, 0.60, and 0.78, combined with other cosmological data sets. The limiting factor in this analysis is the theoretical modeling of the galaxy power spectrum, including nonlinearities, galaxy bias, and redshift-space distortions. In this paper we assess several different methods for modeling the theoretical power spectrum, testing them against the Gigaparsec WiggleZ simulations (GiggleZ). We fit for a base set of six cosmological parameters, $\{{\Omega }_b{h}^2,{\Omega }_{\mathrm{CDM}}{h}^2,H_0,\tau ,A_s,n_s\}$, and five supplementary parameters $\{n_{\mathrm{run}},r,w,{\Omega }_k,\sum _{}^{}{m}_{\nu }\}$. In combination with the cosmic microwave background, our results are consistent with the $\Lambda \mathrm{CDM}$ concordance cosmology, with a measurement of the matter density of ${\Omega }_m=0.29\pm 0.016$ and amplitude of fluctuations ${\sigma }_8=0.825\pm 0.017$. Using WiggleZ data with cosmic microwave background and other distance and matter power spectra data, we find no evidence for any of the extension parameters being inconsistent with their $\Lambda \mathrm{CDM}$ model values. The power spectra data and theoretical modeling tools are available for use as a module for CosmoMC, which we here make publicly available at http://smp.uq.edu.au/wigglez-data. We also release the data and random catalogs used to construct the baryon acoustic oscillation correlation function.

Figure 1

The WiggleZ power spectrum in the four redshift bins, weighted averaged over the seven regions. We artificially offset them in the vertical direction to distinguish them (with the lowest redshift bin at the bottom moving up to highest at the top). At each redshift the line gives the best fit flat-$\Lambda \mathrm{CDM}$ cosmology prediction, convolved with the window function for each region and then averaged over the regions. The shaded region gives the range in wave number of data we used for the analysis.

Figure 2

The WiggleZ covariance matrix in the four redshift bins, as a weighted average over the seven regions.

Figure 3

(Top) A weighted average of the WiggleZ power spectra in the survey regions and redshifts, and the seven models described in Sec. 4a for the best fit cosmology of the best model (G). (Bottom) The same models (with the same meanings for the colors), but now the power spectrum has been rated to the linear prediction. In both plots the shaded region from $k=0.02h{\mathrm{Mpc}}^{-1}$ to $k=0.3h{\mathrm{Mpc}}^{-1}$ is the range of data we are using in our analysis. This shows the divergence of models at large $k$ and the reason why careful modeling is necessary.

Figure 4

1 and $2\sigma$ contours for in the $\{{\Omega }_m,f_b\}$ plane for fits to the GiggleZ power spectra using models A–G. All other cosmological parameters are held fixed at the GiggleZ fiducial cosmology (WMAP 5-year best fit values). The GiggleZ parameter values are marked by a cross. The red ellipses (model E) lie directly on top of the green ones (model B), and so are not visible. This shows that the choice of model has a significant effect on the cosmological constraints from the power spectrum. Our preferred model is the model G, which successfully reproduces the input parameters of the GiggleZ simulation.

Figure 5

Upper: Reduced ${\chi }^2$ of models fitted to the $N$-body simulation halo catalog for the GiggleZ fiducial cosmology values. In absence of systematic errors the models should recover the input cosmology with ${\chi }^2/\mathrm{dof}\simeq 1$. Lower: Difference in reduced ${\chi }^2$ values when using the GiggleZ fiducial cosmological parameters and the best fit values.

Figure 6

1 and $2\sigma$ contours for in the $\{{\Omega }_m,f_b\}$ plane for fits to the WiggleZ power spectra, checking for systematic errors using a number of different data analyses. The red dotted lines (spline fit) lie directly on top of the black (Chebyshev), and so are not visible.

Figure 7

Measurement of ${\Omega }_m{h}^2$ (top) and $f_b$ (bottom) as a function of $k_{\max }$ for the WiggleZ data, with all other cosmological parameters fixed to the WMAP 7-year best fit values, with those two being measured simultaneously.

Figure 8

The probability contours in the $\{{\Omega }_m{h}^2,f_b\}$ plane for WiggleZ alone (black solid line), with all other cosmological parameters fixed to the WMAP 7-year best fit values. We also plot the contours from the WMAP data for a $\Lambda \mathrm{CDM}$ model, marginalizing over all other parameters (blue filled contour). We see good agreement between the two data sets, though the WiggleZ data do favor slightly smaller values of the baryon fraction.

Figure 9

The matter power spectrum plotted for different values of the cosmological parameters. For each plot we fix the other parameters to the fiducial cosmological values while varying only that particular one. The color bar indicates the value of the parameter. The dashed black curve is the power spectrum for the fiducial cosmology, and is the same in all four plots.

Figure 10

The two-dimensional constraints in the $\{{\Omega }_m,H_0\}$ plane for a flat $\Lambda \mathrm{CDM}$ model, using a number of different data sets (see legend). The WiggleZ data are consistent with the CMB data (from WMAP), reducing the size of the error ellipse, but pushing up the preferred values of ${\Omega }_m$.

Figure 11

The two-dimensional constraints in the $\{{\sigma }_8,n_s\}$ plane for a flat $\Lambda \mathrm{CDM}$ model, using a number of different data combinations (see legend). We find that combination of LSS data (from either WiggleZ or SDSS) with the CMB data (WMAP) improves constraints on the spectral index $n_s$ only marginally, but constraints on the amplitude of fluctuations ${\sigma }_8$ by a large amount.

Figure 12

The two-dimensional constraints in the $\{{\Omega }_m,w\}$ plane for a $w\mathrm{CDM}$ model. The supernovae data are far more powerful at measuring distances, having many more data points spread over a range of redshifts, but the addition of the WiggleZ data has an effect on the best fit ${\Omega }_m$ value, pushing it slightly higher.

Figure 13

The two-dimensional constraints in the $\{{\Omega }_m,{\Omega }_{\Lambda }\}$ plane for a $\Lambda \mathrm{CDM}$ model, for a number of different data compilations (see legend). The straight black line gives the location of ${\Omega }_m+{\Omega }_{\Lambda }=1$, i.e., a flat Universe. The WiggleZ data are consistent with the CMB data (from WMAP) with a peak likelihood close to flatness, but have a second likelihood peak for larger values of ${\Omega }_m$, which is away from the flatness line.

Figure 14

The matter power spectrum for two different sets of cosmological parameters, both of which are good fits to the $\Lambda \mathrm{CDM}$ model using $\mathrm{CMB}+\mathrm{WiggleZ}$ data. The solid blue (dark) curve gives the predicted linear $P(k)$ for a high $H_0$, low matter density nearly flat Universe, while the red (light) gives the linear $P(k)$ for a lower $H_0$, higher density, slightly curved Universe. The dashed curves give the same $P(k)$ after the nonlinear effects and window functions have been applied, to compare to the data at $z=0.6$ (black error bars).

Figure 15

The two-dimensional constraints in the $\{{\Omega }_m,{\Omega }_{\Lambda }\}$ plane for a $\Lambda \mathrm{CDM}$ model, comparing the WiggleZ $P(k)$ data with the WiggleZ BAO data (see legend). The straight black line gives the location of ${\Omega }_m+{\Omega }_{\Lambda }=1$, i.e., a flat Universe. The WiggleZ $P(k)$ data are consistent with the BAO from WiggleZ, for the peak likelihood close to flatness, but not for the second peak at high ${\Omega }_m$ values.

Figure 16

The two-dimensional constraints in the $\{{\Omega }_k,w\}$ plane (left) and $\{{\Omega }_k,w\}$ plane (right) for a $w\mathrm{CDM}$ model, using a number of different data sets (see legend). The solid black cross gives the location of flat $\Lambda \mathrm{CDM}$, i.e., a flat Universe with the equation of state $w=-1$.

Figure 17

The two-dimensional constraints in the $\{\sum _{}^{}{m}_{\nu },{\Omega }_m\}$ (left) and $\{\sum _{}^{}{m}_{\nu },H_0\}$ (right) planes for a massive neutrinos model, using a number of different data combinations (see legend).

Figure 18

The two-dimensional constraints in the $\{n_s,n_{\mathrm{run}}\}$ plane. Adding in the WiggleZ data reduces the size of the error bars with a best fit value for the running which is more negative than for WMAP alone ($n_{\mathrm{run}}=-0.033$ for CMB only, whereas it is $n_{\mathrm{run}}=-0.040$ for $\mathrm{CMB}+\mathrm{WiggleZ}$).

Figure 19

The two-dimensional constraints in the $\{n_s,r\}$ plane, for a number of data combinations (see legend). We see that the $\mathrm{CMB}+\mathrm{WiggleZ}$ improves on the upper limit from CMB alone, and gives about the same limit as $\mathrm{CMB}+\mathrm{LSS}$. Combining all three, $\mathrm{CMB}+\mathrm{WiggleZ}+\mathrm{LSS}$, gives the best constraint.