The WiggleZ Dark Energy Survey: measuring the cosmic expansion history using the Alcock-Paczynski test and distant supernovae

TL;DR

This work presents a model-independent reconstruction of the cosmic expansion history by combining Alcock–Paczynski distortions measured in the WiggleZ galaxy survey with Type Ia supernova distances. The authors convert AP measurements of $F(z)=(1+z)D_A(z)H(z)/c$ into $H(z)/[H_0(1+z)]$ using the SN-based distance-redshift relation, obtaining 10–15% precision in four redshift bins between $0.1<z<0.9$ and providing direct evidence for acceleration without assuming a specific cosmological model. They further perform a non-parametric reconstruction of $D_A(z)$, $H(z)$, ${ m Om}(z)$, and $q(z)$ via an iterative method, finding ${ m Om}(z)$ consistent with a flat $oldsymbol{ m  m}$CDM value of about $0.29$ and a consistent $H(z)$ history. The results strongly support a cosmological-constant–driven acceleration and demonstrate the power of combining geometric AP tests with SN data to recover the expansion history in a curvature-insensitive way, with implications for future large-volume surveys.

Abstract

Astronomical observations suggest that today's Universe is dominated by a dark energy of unknown physical origin. One of the most notable consequences in many models is that dark energy should cause the expansion of the Universe to accelerate: but the expansion rate as a function of time has proven very difficult to measure directly. We present a new determination of the cosmic expansion history by combining distant supernovae observations with a geometrical analysis of large-scale galaxy clustering within the WiggleZ Dark Energy Survey, using the Alcock-Paczynski test to measure the distortion of standard spheres. Our result constitutes a robust and non-parametric measurement of the Hubble expansion rate as a function of time, which we measure with 10-15% precision in four bins within the redshift range 0.1 < z < 0.9. We demonstrate that the cosmic expansion is accelerating, in a manner independent of the parameterization of the cosmological model (although assuming cosmic homogeneity in our data analysis). Furthermore, we find that this expansion history is consistent with a cosmological-constant dark energy.

Figures (7)

• Figure 1: The galaxy power spectrum amplitude 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 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. In the absence of redshift-space distortions, the model contours would be horizontal lines if the fiducial cosmology was equal to the true cosmology.
• Figure 2: This Figure displays the joint likelihood of the Alcock-Paczynski scale distortion parameter $F(z)$ relative to the fiducial value $F_{\rm fid}$, and the growth rate quantified by $f \, \sigma_8(z)$, obtained from fits to the 2D galaxy power spectra of the WiggleZ Dark Energy Survey in four redshift slices. In order to produce this Figure we marginalized over the linear galaxy bias $b^2$ and the pairwise velocity dispersion $\sigma_v$. There is some degeneracy between $F$ and $f \, \sigma_8$ but their characteristic dependence on the angle to the line-of-sight is sufficiently different that both parameters may be successfully extracted. The probability density is plotted as both greyscale and contours enclosing $68\%$ and $95\%$ of the total likelihood. The solid circles indicate the parameter values in our fiducial cosmological model.
• Figure 3: This Figure quantifies the amplitude of systematic errors in our measurements of the scale distortion parameter $F(z)$ in four redshift slices relative to the fiducial value $F_{\rm fid}$, marginalized over the growth rate $f$, galaxy bias $b^2$ and pairwise velocity dispersion $\sigma_v$ (where appropriate). The solid black data points show our default measurement using the redshift-space distortion model provided by Jennings et al. (2011) fitting to the wavenumber range $0 < k < k_{\rm max} = 0.2 \, h$ Mpc$^{-1}$. The remaining data points illustrate the effects of varying these assumptions: using $k_{\rm max} = 0.3 \, h$ Mpc$^{-1}$ [red], $k_{\rm max} = 0.1 \, h$ Mpc$^{-1}$ [green], adding the pairwise velocity dispersion as a free parameter [blue], fitting using the large-scale Kaiser limit formula of Equation \ref{['eqpkap2']} [cyan], and using the data itself to define the real-space power spectrum via a polynomial fit to an angle-averaged measurement of $P(k)$ [magenta]. Each subsequent data point is slightly offset in redshift for clarity.
• Figure 4: This Figure displays the best-fitting 3rd-order polynomial to the Union-2 compilation of supernovae data, normalized as a plot of angular-diameter distance versus redshift.
• Figure 5: This Figure displays our measurement of the evolution of the cosmic expansion rate using Alcock-Paczynski and supernovae data. The expansion rate is displayed using the value of $\dot{a}/\dot{a}_0 = H(z)/[H_0(1+z)]$; accelerating expansion implies a decrease in the value of this quantity with increasing redshift. The black data points are obtained by combining Alcock-Paczynski measurements of $(1+z) D_A(z) H(z)/c$ in four independent redshift slices with supernovae distance determinations of $D_L(z) H_0/c$ at these redshifts, and are independent of curvature. The thicker, blue data points result from applying the distance reconstruction method of Shafieloo et al. (2006) to both the supernovae and Alcock-Paczynski data, producing optimal errors at both low and high redshift but making the additional assumptions of zero spatial curvature and that $D_A(z)$ may be expressed in terms of an integral over $1/H(z)$. Predictions are plotted for three different models: a fiducial $\Lambda$CDM model with $\Omega_{\rm m} = 0.27$ (solid line), an Einstein de-Sitter model with $\Omega_{\rm m} = 1$ (dashed line), and a "coasting" model where $\dot{a} =$ constant (dotted line).