Baryon Acoustic Oscillations in the Sloan Digital Sky Survey Data Release 7 Galaxy Sample

TL;DR

This study analyzes BAO in the SDSS DR7 galaxy sample (LRG and Main) combined with 2dFGRS to measure the distance–redshift relation through a series of redshift slices. By modeling the BAO as a damped linear signal with a flexible spline in $D_V(z)$ and validating the method with 10^4 log-normal mocks, the authors extract a robust measurement $d_{0.275}=r_s(z_d)/D_V(0.275)=0.1390\pm0.0037$ and a distance ratio $D_V(0.35)/D_V(0.2)=1.736\pm0.065$, with a $\sim3.6\sigma$ BAO detection. Integrating these BAO constraints with WMAP5 data and SN observations yields tight cosmological parameter constraints, notably $\Omega_m\approx0.286\pm0.018$ and $H_0\approx68.2\pm2.2\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$ in a flat $\Lambda$CDM framework, and modest allowances for curvature and a constant $w$. The results demonstrate BAO’s power as a robust, low-systematics probe of cosmic expansion, largely independent of high-z dark-energy behavior, and underscore the value of large redshift surveys for precision cosmology.

Abstract

The spectroscopic Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) galaxy sample represents the final set of galaxies observed using the original SDSS target selection criteria. We analyse the clustering of galaxies within this sample, including both the Luminous Red Galaxy (LRG) and Main samples, and also include the 2-degree Field Galaxy Redshift Survey (2dFGRS) data. Baryon Acoustic Oscillations are observed in power spectra measured for different slices in redshift; this allows us to constrain the distance--redshift relation at multiple epochs. We achieve a distance measure at redshift z=0.275, of r_s(z_d)/D_V(0.275)=0.1390+/-0.0037 (2.7% accuracy), where r_s(z_d) is the comoving sound horizon at the baryon drag epoch, D_V(z)=[(1+z)^2D_A^2cz/H(z)]^(1/3), D_A(z) is the angular diameter distance and H(z) is the Hubble parameter. We find an almost independent constraint on the ratio of distances D_V(0.35)/D_V(0.2)=1.736+/-0.065, which is consistent at the 1.1sigma level with the best fit Lambda-CDM model obtained when combining our z=0.275 distance constraint with the WMAP 5-year data. The offset is similar to that found in previous analyses of the SDSS DR5 sample, but the discrepancy is now of lower significance, a change caused by a revised error analysis and a change in the methodology adopted, as well as the addition of more data. Using WMAP5 constraints on Omega_bh^2 and Omega_ch^2, and combining our BAO distance measurements with those from the Union Supernova sample, places a tight constraint on Omega_m=0.286+/-0.018 and H_0 = 68.2+/-2.2km/s/Mpc that is robust to allowing curvature and non-Lambda dark energy. This result is independent of the behaviour of dark energy at redshifts greater than those probed by the BAO and supernova measurements. (abridged)

Figures (16)

• Figure 1: Average power spectra recovered from the Log-Normal catalogues (solid lines) compared with the data power spectra (solid circles with 1-$\sigma$ errors) for the six samples in Table \ref{['tab:slices']}. The errors on the data were calculated from the diagonal elements of the covariance matrix calculated from these log-normal catalogues. The power spectra have been offset by 0.5dex for clarity, with the upper power spectrum having the correct normalisation.
• Figure 2: Average likelihood contours recovered from the analysis of three power spectra (top panel) and six power spectra (bottom panel) measured from 1000 Log-Normal density fields. Contours are plotted for $-2\ln{\cal L}=2.3,\,6.0,\,9.2$, corresponding to two-parameter confidence of 68%, 95% and 99% for a Gaussian distribution. Contours were calculated after increasing the errors on the power spectrum band-powers as described in the text. Solid circles mark the locations of the likelihood maxima closest to the true cosmology. We have plotted the likelihood surface as a function of $D_V(z) / {\rm Mpc}$, for fixed $r_s(z_d)=154.7\,{\rm Mpc}$, to show distance errors if the comoving sound horizon is known perfectly. The values of $D_V$ for our input cosmology are shown by the vertical and horizontal solid lines.
• Figure 3: BAO recovered from the data for each of the redshifts slices (solid circles with 1-$\sigma$ errors). These are compared with BAO in our default $\Lambda$CDM model (solid lines).
• Figure 4: Likelihood contour plots for fits of two $D_V(z)$ cubic spline nodes at $z=0.2$ and $z=0.35$, calculated for our default analysis using six power spectra, uber-calibration, a fixed BAO damping scale of $D_{\rm damp}=10\,h^{-1}\,{\rm Mpc}$, and for all SDSS and non-overlapping 2dFGRS data. Solid contours are plotted for $-2\ln{\cal L}/{\cal L}_{\rm true}<2.3,\,6.0,\,9.3$, which for a multi-variate Gaussian distribution with two degrees of freedom correspond to 68%, 95% and 99% confidence intervals. Likelihoods were adjusted to match these Gaussian confidence intervals as described in Section \ref{['sec:bao_ln']}. We have plotted the likelihood surface as a function of $D_V(z) / {\rm Mpc}$, for fixed $r_s(z_d)=154.7\,{\rm Mpc}$, to show distance errors if the comoving sound horizon is known perfectly. We also show a multi-variate Gaussian fit to this likelihood surface (dashed contours). The values of $D_V$ for a flat $\Lambda$CDM cosmology with $\Omega_m=0.25$, $h=0.72$, & $\Omega_bh^2=0.0223$ are shown by the vertical and horizontal solid lines.
• Figure 5: Cosmological constraints on $\Lambda$CDM cosmologies (upper panel) and flat CDM models where we allow $w$ to vary (lower panel), from WMAP5 (blue), Union supernova (green) and our constraint on $r_s/D_V(0.275)$ (solid contours). Contours are plotted for $-2\ln{\cal L}/{\cal L}_{\rm true}<2.3,\,6.0$, corresponding to 68% and 95% confidence intervals. The dashed lines show flat models (upper panel) and $\Lambda$ models (lower panel).