The WiggleZ Dark Energy Survey: Joint measurements of the expansion and growth history at z < 1

TL;DR

This work jointly determines the distance-redshift relation and expansion rate at z<1 by combining WiggleZ BAO and Alcock-Paczynski measurements, deriving D_A(z) and H(z) in three redshift slices with ~7–9% precision. Covariances among A, F, and fσ8 are quantified using 400 lognormal mock realizations to enable robust joint fits and a nine-parameter covariance. By augmenting WiggleZ with other BAO and SNe data, the authors reconstruct H(z) as a stepwise function in 9 bins (Δz=0.1) and test against ΛCDM, wCDM, and kinematical models, finding consistency with a cosmological-constant-driven expansion. The results demonstrate the value of combining BAO and AP measurements to tightly constrain the expansion history and growth, while reducing inter-bin covariance compared to distance-only probes.

Abstract

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 D_A(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/Mpc at these three redshifts. Further combining our results with other baryon acoustic oscillation and distant supernovae datasets, we use a Monte Carlo Markov Chain technique to determine the evolution of the Hubble parameter H(z) as a stepwise function in 9 redshift bins of width dz = 0.1, also marginalizing over the spatial curvature. Our measurements of H(z), which have precision better than 7% 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.

Figures (11)

• Figure 1: The joint likelihood of the Alcock-Paczynski scale distortion parameter $F(z) \equiv (1+z) D_A(z) H(z)/c$ and the normalized growth rate quantified by $f \, \sigma_8(z)$, obtained from fits to the 2D galaxy power spectra of the WiggleZ Dark Energy Survey in three overlapping redshift slices $0.2 < z < 0.6$, $0.4 < z < 0.8$ and $0.6 < z < 1.0$. This Figure was produced by marginalizing over the linear bias factor $b^2$. The probability density is plotted as contours enclosing $68.27\%$ and $95.45\%$ of the total likelihood. The solid circles indicate the parameter values in a fiducial flat $\Lambda$CDM cosmological model with parameters $\Omega_{\rm m} = 0.27$, $\sigma_8 = 0.8$.
• Figure 2: Correlations of the parameters $A(z)$, $F(z)$ and $f \, \sigma_8(z)$ when each parameter is fitted to pairs of the three overlapping WiggleZ redshift slices. The Alcock-Paczynski distortion parameter $F$ is plotted relative to its value in the fiducial cosmology, $F_{\rm fid}$. Each small dot represents the best-fitting values of the parameters using the correlation functions and power spectra measured from 400 independent lognormal realizations. The red ellipses represent the derived covariances between the parameter fits, and the solid red circle is the input fiducial model of the lognormal realizations. The correlation coefficient $r$ is quoted in the bottom left-hand corner of each panel, and is consistent with zero in the second column when non-overlapping redshift slices are used.
• Figure 3: Correlations between different pairs of the parameters $A(z)$, $F(z)$ and $f \, \sigma_8(z)$ fitted to the three WiggleZ redshift slices. The Alcock-Paczynski distortion parameter $F$ is plotted relative to its value in the fiducial cosmology, $F_{\rm fid}$. Each small dot represents the best-fitting values of the parameters using the correlation functions and power spectra measured from 400 independent lognormal realizations. The red ellipses represent the derived covariances between the measurements, and the solid red circle is the input fiducial model of the lognormal realizations. The correlation coefficient $r$ is quoted in the bottom left-hand corner of each panel. Although the strongest correlation is obtained between $F(z)$ and $f \, \sigma_8(z)$, weaker but non-zero correlations are measured between both of these parameters and $A(z)$.
• Figure 4: The 1D distribution of the best-fitting parameters for 400 lognormal realizations for the second redshift slice, compared to the adopted multivariate Gaussian model for the covariance. The full distribution does not contain significant wings that might cause confidence regions to be under-estimated in subsequent cosmological parameter fits.
• Figure 5: The joint likelihood of fits of $D_A(z)$ and $H(z)$ to the baryon acoustic peak and Alcock-Paczynski distortions in each of three overlapping WiggleZ redshift slices. The two contour levels in each case enclose regions containing $68.27\%$ and $95.45\%$ of the total likelihood. A flat $\Lambda$CDM model prediction for cosmological parameters $\Omega_{\rm m} = 0.27$ and $h = 0.71$ is plotted as the solid line, with circles representing the effective redshifts of the three data slices.