The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Testing gravity with redshift-space distortions using the power spectrum multipoles

TL;DR

This work uses the CMASS-DR11 galaxy sample to perform a Fourier-space, multipole-based analysis of anisotropic clustering, leveraging BAO, redshift-space distortions, and the Alcock-Paczynski effect to jointly constrain geometry and growth. The authors implement a self-consistent treatment of the survey window and integral constraint using the Yamamoto estimator and a perturbation-theory–driven eTNS model, validated with 999 QPM mocks and N-body tests. They find precise measurements of $D_V/r_s$, $F_{ m AP}$, and $f\sigma_8$ at $z_{\rm eff}=0.57$, with a systematic floor on $f\sigma_8$ of about 3.1% and a Planck-compatible geometric signal but a modest tension in the growth rate relative to GR. By combining CMASS with Planck, they derive a growth index $\gamma=0.77^{+0.12}_{-0.10}$, indicating potential tension with GR, while CMASS alone yields a competitive constraint on $\sigma_8=0.731\pm0.052$, demonstrating the power of low-redshift clustering as an independent probe of structure formation and gravity.

Abstract

We analyse the anisotropic clustering of the Baryon Oscillation Spectroscopic Survey (BOSS) CMASS Data Release 11 (DR11) sample, which consists of $690\,827$ galaxies in the redshift range $0.43 < z < 0.7$ and has a sky coverage of $8\,498\,\text{deg}^2$. We perform our analysis in Fourier space using a power spectrum estimator suggested by Yamamoto et al. (2006). We measure the multipole power spectra in a self-consistent manner for the first time in the sense that we provide a proper way to treat the survey window function and the integral constraint, without the commonly used assumption of an isotropic power spectrum and without the need to split the survey into sub-regions. The main cosmological signals exploited in our analysis are the Baryon Acoustic Oscillations and the signal of redshift space distortions, both of which are distorted by the Alcock-Paczynski effect. Together, these signals allow us to constrain the distance ratio $D_V(z_{\rm eff})/r_s(z_d) = 13.89\pm 0.18$, the Alcock-Paczynski parameter $F_{\rm AP}(z_{\rm eff}) = 0.679\pm0.031$ and the growth rate of structure $f(z_{\rm eff})σ_8(z_{\rm eff}) = 0.419\pm0.044$ at the effective redshift $z_{\rm eff}=0.57$. We did not find significant systematic uncertainties for $D_V/r_s$ or $F_{\rm AP}$ but include a systematic error for $fσ_8$ of $3.1\%$. Combining our dataset with Planck to test General Relativity (GR) through the simple $γ$-parameterisation, reveals a $\sim 2σ$ tension between the data and the prediction by GR. The tension between our result and GR can be traced back to a tension in the clustering amplitude $σ_8$ between CMASS and Planck.

Figures (17)

• Figure 1: Summary of different tests of General Relativity (GR) as a function of distance scale (bottom axis) and densities (top axis). The standard model of cosmology seems to run into problems (dark matter, dark energy) at large scales. Because these problems could indicate a breakdown of GR we need to test GR on large scales. Two probes which can do this are redshift space distortions (RSD) and lensing. While RSD measures the Newtonian potential $\Psi$, lensing measures the sum of the metric potentials $\Phi + \Psi$. However, any modification of gravity needs to pass the very precise tests on smaller scales (Pound & Rebka experiment Pound:1960zz, Gravity Probe A, Vessot:1980zz, Hulse-Taylor binary pulsar Hulse:1974eb, see Will:2005va for a complete list). Note that the error bars for Gravity Probe A and the Hulse-Taylor binary pulsar are smaller than the data points in this plot. In this analysis we perform a $\Lambda$CDM consistency test (blue data point), where we use the CMASS-DR11 power spectrum multipoles together with Planck Ade:2013zuv to tests GR on scales of $\sim 30\,$Mpc (see section \ref{['sec:consistency']}).
• Figure 2: The CMASS-DR11 North Galactic Cap (top) and South Galactic Cap (bottom) sky coverage. The grey region indicates the final footprint of the survey (DR12). The colours indicate the completeness in the regions included in our analysis.
• Figure 3: The measured CMASS-DR11 monopole (top) and quadrupole (bottom) power spectra. The black data points are the measurement of the North Galactic Cap (NGC) and the red data points are the measurement of the South Galactic Cap (SGC) of CMASS-DR11. The black data points have been shifted by $\Delta k = 0.001h/$Mpc to the right for clarity. The error bars are the diagonal of the covariance matrix. Because of the smaller volume in the SGC the error bars are larger by a factor of $\sim 1.6$. The solid black and red lines represent the best fitting power spectra for the NGC (black) and SGC (red) respectively (fitting range $k = 0.01$ - $0.20h/$Mpc, see section \ref{['sec:fit']}). The red and black lines are based on the same cosmology and only differ in the effect of the window function (see section \ref{['sec:win']}). The lower two panels show the difference between the measured monopole and the best fitting monopole (middle panel) and the measured quadrupole and the best fitting quadrupole (bottom panel), both relative to the diagonal elements of the covariance matrix. We fit the monopole and quadrupole simultaneously. The best fitting $\chi^2$ is $66.6+73.9 = 140.5$ (NGC + SGC) for $152$ bins and $7$ free parameters (see Table \ref{['tab:para']}). The contribution to $\chi^2$ from the monopole and quadrupole alone is given in the middle and lower panel, for comparison.
• Figure 4: The power spectrum monopole (top) and quadrupole (bottom) of the $999$ QPM mock catalogues (grey lines) for the North Galactic Cap (left) and the South Galactic Cap (right), relative to an Eisenstein:1997ik no-BAO monopole power spectrum. We plot the power spectrum without the shot noise subtraction, since this way, the scatter closely represents the diagonal of the covariance matrix. The red lines show the mean of all mock catalogues with the error representing the variance around the mean. The blue lines show the measured CMASS-DR11 power spectra.
• Figure 5: The correlation matrix for the NGC (left) and SGC (right) of CMASS-DR11. The colour indicates the level of correlation, where red represents high correlation, blue represents high anti-correlation and green represents no-correlation. The correlation between the bins in the monopole is shown in the lower left hand corner, while the correlation between the $k$-bins in the quadrupole is shown in the upper right hand corner. The upper left hand corner and the lower right hand corner show the cross-correlations.