The 6dF Galaxy Survey: z \approx 0 measurement of the growth rate and sigma_8 (1204.4725v1)

Abstract: We present a detailed analysis of redshift-space distortions in the two-point correlation function of the 6dF Galaxy Survey (6dFGS). The K-band selected sub-sample which we employ in this study contains 81971 galaxies distributed over 17000deg^2 with an effective redshift z = 0.067. By modelling the 2D galaxy correlation function, xi(r_p,pi), we measure the parameter combination f(z)sigma_8(z) = 0.423 +/- 0.055. Alternatively, by assuming standard gravity we can break the degeneracy between sigma_8 and the galaxy bias parameter, b. Combining our data with the Hubble constant prior from Riess et al (2011), we measure sigma_8 = 0.76 +/- 0.11 and Omega_m = 0.250 +/- 0.022, consistent with constraints from other galaxy surveys and the Cosmic Microwave Background data from WMAP7. Combining our measurement of fsigma_8 with WMAP7 allows us to test the relationship between matter and gravity on cosmic scales by constraining the growth index of density fluctuations, gamma. Using only 6dFGS and WMAP7 data we find gamma = 0.547 +/- 0.088, consistent with the prediction of General Relativity. We note that because of the low effective redshift of 6dFGS our measurement of the growth rate is independent of the fiducial cosmological model (Alcock-Paczynski effect). We also show that our conclusions are not sensitive to the model adopted for non-linear redshift-space distortions. Using a Fisher matrix analysis we report predictions for constraints on fsigma_8 for the WALLABY survey and the proposed TAIPAN survey. The WALLABY survey will be able to measure fsigma_8 with a precision of 4-10%, depending on the modelling of non-linear structure formation. This is comparable to the predicted precision for the best redshift bins of the Baryon Oscillation Spectroscopic Survey (BOSS), demonstrating that low-redshift surveys have a significant role to play in future tests of dark energy and modified gravity.

• The paper presents a direct fσ8 measurement of 0.423±0.055 from 6dFGS redshift-space distortions.
• It uses detailed modeling of the 2D galaxy correlation function to account for wide-angle and non-linear effects.
• Results consistent with GR and WMAP7 set a robust baseline for future low-redshift surveys like WALLABY and TAIPAN.

Analysis of Redshift-Space Distortions in the 6dF Galaxy Survey

The paper by Beutler et al. presents an in-depth examination of redshift-space distortions (RSDs) in the two-point correlation function of the 6dF Galaxy Survey (6dFGS), focusing on measurements of the growth rate of cosmic structures at low redshift ($z_{\rm eff} \approx 0.067$). This analysis explores the combination of the growth rate, $f(z_{\rm eff})$, and the root mean square of matter fluctuations, $\sigma_8(z_{\rm eff})$, revealing $$f(z_{\rm eff})\sigma_8(z_{\rm eff}) = 0.423 \pm 0.055$$. The paper provides substantial insights into the local Universe and contributes to cosmological theories, particularly regarding dark energy and gravity.

Methodological Approach

The paper employs the 6dFGS's large $K$-band selected sample of 81,971 galaxies, covering a sky area of 17,000 square degrees. The effective redshift is sufficiently low to make the results robust against the Alcock-Paczynski effect, often encountered in similar analyses at higher redshifts. The authors model the 2D galaxy correlation function, $\xi(r_p,\pi)$, considering wide-angle effects and non-linear RSDs. Various models, including the Scoccimarro framework, are used to extend the linear theory to accommodate non-linear contributions effectively.

A particular strength lies in the examination of the parameter $$g_{\theta}(z_{\rm eff}) = f(z_{\rm eff})\sigma_8(z_{\rm eff})$$, tested against predictions from General Relativity (GR). Using a Fisher matrix analysis, the paper predicts constraints for future low-redshift galaxy surveys (like WALLABY and TAIPAN), indicating their essential role in future cosmological tests.

Numerical Results and Implications

The results present $g_{\theta}(z_{\rm eff}) = 0.423\pm0.055$, translating into significant cosmological implications when tested against the WMAP7 Cosmic Microwave Background (CMB) data. The paper finds $\sigma_8 = 0.76 \pm 0.11$ and $\Omega_m = 0.250 \pm 0.022$, consistent with other survey constraints, reinforcing the standard cosmological model. By integrating CMB inputs and the derived growth rate from 6dFGS, the growth index $\gamma$ is calculated as $0.547\pm 0.088$, in line with GR expectations.

This work provides a compelling confirmation of the GR-predicted growth index at low redshift. However, the measurement of the growth of structure, independent of cosmological model dependencies, distinctly supports GR while setting a baseline for discrepancies that could advocate alternative gravity theories.

Theoretical and Practical Considerations

Practically, the paper points toward future observations with the WALLABY and TAIPAN surveys, which promise precision on par with high-redshift surveys concerning dark energy and modified gravity. The WALLABY survey, anticipated to surpass in precision due to its higher galaxy density and coverage, is predicted to measure $f\sigma_8$ with accuracy significantly enhancing the current 6dFGS results.

Theoretically, the robustness of $g_{\theta}(z_{\rm eff})$, independent of fiducial cosmology, highlights its utility in cross-verifying results across different datasets and redshifts. This independence provides a reliable measure against which the evolution of cosmic structure can be assessed over cosmic time scales.

Conclusion

In summation, Beutler et al.'s research is an essential contribution to contemporary cosmological models, substantiating the growth of structures in the Universe coherently predicted by GR. The provided methodology, enriched by data from low-redshift surveys, is crucial for future developments in cosmology, offering pathways to refine the constraints on fundamental cosmological parameters. The insights gained from 6dFGS, coupled with prospective future survey data, foster a promising horizon for understanding the Universe's composition, dynamics, and the governing laws on grand scales.