The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: measurements of the growth of structure and expansion rate at z=0.57 from anisotropic clustering (1203.6641v1)

Abstract: We analyze the anisotropic clustering of massive galaxies from the Sloan Digital Sky Survey III Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 9 (DR9) sample, which consists of 264,283 galaxies in the redshift range 0.43 < z < 0.7 spanning 3,275 square degrees. Both peculiar velocities and errors in the assumed redshift-distance relation ("Alcock-Paczynski effect") generate correlations between clustering amplitude and orientation with respect to the line-of-sight. Together with the sharp baryon acoustic oscillation (BAO) standard ruler, our measurements of the broadband shape of the monopole and quadrupole correlation functions simultaneously constrain the comoving angular diameter distance (2190 +/- 61 Mpc) to z=0.57, the Hubble expansion rate at z=0.57 (92.4 +/- 4.5 km/s/Mpc), and the growth rate of structure at that same redshift (d sigma8/d ln a = 0.43 +/- 0.069). Our analysis provides the best current direct determination of both DA and H in galaxy clustering data using this technique. If we further assume a LCDM expansion history, our growth constraint tightens to d sigma8/d ln a = 0.415 +/- 0.034. In combination with the cosmic microwave background, our measurements of DA, H, and growth all separately require dark energy at z > 0.57, and when combined imply \Omega_{\Lambda} = 0.74 +/- 0.016, independent of the Universe's evolution at z<0.57. In our companion paper (Samushia et al. prep), we explore further cosmological implications of these observations.

• The paper leverages the monopole and quadrupole moments of the galaxy correlation function to measure the expansion rate and growth of structure at z=0.57.
• It utilizes a robust sample of 264,283 CMASS galaxies over 3275 square degrees, effectively accounting for redshift-space distortions and the Alcock-Paczynski effect.
• The results reinforce the ΛCDM model and offer key constraints that support future integration with complementary cosmological probes.

Anisotropic Clustering in CMASS Galaxies: Cosmological Implications

The paper by Reid et al. presents a detailed analysis of the anisotropic clustering of galaxies using the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 9 CMASS sample. The primary aim of this work is to constrain cosmological parameters such as the growth rate of structure and the expansion rate of the universe at redshift $z=0.57$ through measurements of the two-dimensional galaxy correlation function.

Methodology and Data

The analysis is grounded on a comprehensive dataset that spans over 3275 square degrees and comprises 264,283 galaxies. The anisotropic clustering of these galaxies is attributed to redshift-space distortions (RSD) due to peculiar velocities and the Alcock-Paczynski (AP) effect owing to errors in the assumed redshift-distance relation. The authors employ a robust theoretical model to interpret the monopole and quadrupole moments of the correlation function, $\xi_0(s)$ and $\xi_2(s)$, leveraging perturbation theory for non-linear clustering and velocity statistics.

Numerical Results

One of the key results from this analysis is the determination of the comoving angular diameter distance $D_A = 2190 \pm 61$ Mpc, and the Hubble expansion rate $H = 92.4 \pm 4.5$ km s$^{-1}$ Mpc$^{-1}$ at $z=0.57$. Remarkably, they measure the growth rate of structure as $d\sigma_8/d\ln a = 0.43 \pm 0.069$, which further tightens to $0.415 \pm 0.034$ when a $\Lambda$CDM expansion history is assumed. These results provide independent constraints that substantiate the presence of dark energy at $z > 0.57$ when combined with the cosmic microwave background (CMB) data.

Implications and Theoretical Insights

The findings of this work are significant both in terms of practical application and theoretical exploration. Practically, the results reinforce the $\Lambda$CDM model as they align closely with expectations from widely accepted cosmological parameters, enhancing the credibility of large-scale structure surveys in cosmology. Theoretically, the analysis demonstrates the effective use of galaxy clustering as a tool for probing the universe's geometry and structure growth, offering insights that could be crucial for evaluating modifications to general relativity or alternative dark energy models.

Future Directions

The authors acknowledge areas for improvement that could refine future analyses, including enhanced modeling of non-linear effects and a more precise treatment of observational systematics. Continuing to refine these methods and extend the dataset, such as with the forthcoming data from projects like the Dark Energy Spectroscopic Instrument (DESI), will allow for even tighter constraints on cosmological parameters. Moreover, integrating these findings with complementary probes of cosmic structure, like weak lensing and cluster abundance, could open new avenues for testing the cosmological model and exploring the nature of dark energy further.

In summary, this paper by Reid et al. represents a key step in the precise measurement of cosmic distances and growth rates using galaxy clustering, anchored firmly within the contemporary cosmological framework provided by the $\Lambda$CDM model.