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

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.

• The paper presents precise measurements of cosmic growth using redshift-space distortions across four redshift bins.
• It applies a flat ΛCDM model (Ωm = 0.27) and achieves about 10% precision in analyzing galaxy clustering and velocity divergence.
• The study introduces the first measurements of the velocity divergence power spectrum, paving the way for testing dark energy and modified gravity theories.

Insights into the Growth Rate of Cosmic Structure from the WiggleZ Dark Energy Survey

The paper, "The WiggleZ Dark Energy Survey: the growth rate of cosmic structure since redshift z=0.9," presents an examination of the growth of large-scale cosmic structures using data from the WiggleZ Dark Energy Survey. This survey uniquely covers the redshift range $0.1 < z < 0.9$, offering a comprehensive look at the evolution of the Universe's structure over a significant period during which dark energy began to play a dominant role in cosmic dynamics.

Methodology and Data Analysis

The authors utilize redshift-space distortions in the galaxy power spectrum to achieve precise measurements of the growth rate of cosmic structures across four discrete redshift bins. The survey data is robustly fitted to a flat $\Lambda$CDM cosmological model featuring a matter density parameter of $\Omega_m = 0.27$. The methodology applied ensures a precision of approximately 10%, positioning these findings as particularly reliable when cross-examined across over 150,000 galaxies sampled in various sky regions.

Further, the study extracts the first measurements of the power spectrum of the velocity divergence field, $P_{\theta\theta}(k)$, as a function of redshift. These findings provide critical insights through the assumption that $$P_{\delta\theta}(k) = -\sqrt{P_{\delta\delta}(k)P_{\theta\theta}(k)}$$, aligning with a deterministic bias model over many scales.

Numerical Results and Observational Outcomes

Significant numerical results indicate that the WiggleZ galaxy power spectrum manifests the influence of both density and velocity fields, necessitating various theoretical models to interpret these effects accurately. The authors compare empirical models and perturbation theory techniques to extract the growth rate, finding that the Taruya et al. model and the results from Jennings et al. provide consistent results across scales $k < 0.3h \text{ Mpc}^{-1}$.

The calculated growth rate $f(z)$ at the four effective redshifts $z_{\text{eff}} = (0.22, 0.41, 0.60, 0.78)$ were found to be $$f(z) = (0.60±0.10, 0.70±0.07, 0.73±0.07, 0.70±0.08)$$, respectively. These values suggest an alignment with a flat $\Lambda$CDM model, reinforcing its ability to describe the growth of cosmic structures with reasonable accuracy.

Implications and Future Prospects

This research has significant implications for our understanding of the Universe's expansion and the role of dark energy. By offering a new avenue through which to evaluate the growth rate of cosmic structures—complementary to more traditional measures such as supernovae and baryon acoustic oscillations—the WiggleZ survey enhances our ability to discern differing cosmological models.

Looking ahead, this work lays a foundation for future observational campaigns aiming to refine these measurements further. As the field of cosmology advances, the potential to integrate these findings with modified gravity models or alternative theories of dark energy could yield groundbreaking insights. Coupling these observations with CMB data could reveal much about the nature of dark energy and the comprehensive dynamics driving cosmic acceleration.

In summary, this research not only enriches our understanding of cosmic structure development but also opens new pathways for challenging existing cosmological theories with increasingly precise empirical data. As observational accuracy improves, so too does our capacity to unravel the complex interplay of forces shaping the Universe.