Measuring the matter density using baryon oscillations in the SDSS

TL;DR

Problem: measure the matter density parameter $\\Omega_M$ using baryon acoustic oscillations (BAO) in the SDSS galaxy power spectrum. Approach: model the spectrum as a two-component mixture consisting of a smooth broadband shape and a high-frequency BAO term derived from a CDM transfer function, and constrain $\\Omega_M$ by comparing to 31 flat $\\Lambda$ models with covariances from $2000$ log-normal mocks per model, while marginalizing over $h$ and $\\Omega_b h^2$ constraints. Key results: detection of BAO at 99.74% confidence; in combination with CMB constraints, yields $\\Omega_M = 0.256^{+0.029}_{-0.024}$ (from WMAP angular scale) or $\\Omega_M = 0.256^{+0.020}_{-0.022}$ (from CMB $\\Omega_M h^2$), consistent with a flat $\\Lambda$ universe and independent of the broadband power shape. Significance: demonstrates BAO as a clean, powerful cosmological distance ruler with strong agreement between low-redshift BAO measurements and CMB-based inferences, paving the way for precision cosmology with future surveys.

Abstract

We measure the cosmological matter density by observing the positions of baryon acoustic oscillations in the clustering of galaxies in the Sloan Digital Sky Survey (SDSS). We jointly analyse the main galaxies and LRGs in the SDSS DR5 sample, using over half a million galaxies in total. The oscillations are detected with 99.74% confidence (3.0sigma assuming Gaussianity) compared to a smooth power spectrum. When combined with the observed scale of the peaks within the CMB, we find a best-fit value of Omega_m=0.256+0.029-0.024 (68% confidence interval), for a flat Lambda cosmology when marginalising over the Hubble parameter and the baryon density. This value of the matter density is derived from the locations of the baryon oscillations in the galaxy power spectrum and in the CMB, and does not include any information from the overall shape of the power spectra. This is an extremely clean cosmological measurement as the physics of the baryon acoustic oscillation production is well understood, and the positions of the oscillations are expected to be independent of systematics such as galaxy bias.

Figures (3)

• Figure 1: Results from fitting to 200 mock linear CDM power spectra calculated assuming $h=0.73$, $\Omega_M=0.24$ and $n_s=0.96$, with our two component spline + BAO model. We plot the average ratio between input power and spline fit from 100 mock CDM power spectra with no baryon oscillations (open circles with 1$\sigma$ errors), and 100 mocks with baryon oscillations assuming $\Omega_b/\Omega_M=0.174$ (solid circles with 1$\sigma$ errors). The expected residual in each case is shown by the solid lines. From these fits, we find that the difference between input and recovered power $\Delta P(k)/P(k)<0.015$ for $0.01<k<0.3\,h\,{\rm Mpc}^{-1}$, a level well below the current experimental error (grey shaded region).
• Figure 2: The ratio of the power spectra calculated from the SDSS to the smooth cubic spline fit that we use to model the overall shape of the measured power spectra (solid circles with 1-$\sigma$ errors). Data are plotted using five flat $\Lambda$ cosmological models to convert from redshift to comoving distance, with matter densities given in each panel. For comparison, in each panel we also plot the BAO predicted by a CDM model with the same matter density, $h=0.73$, and a 17% baryon fraction (solid lines). The dashed lines show the same models without the low-redshift small-scale damping term. As can be seen, the observed oscillations approximately match those predicted by this model for $0.2\le\Omega_M\le0.3$, but fail for higher or lower matter densities.
• Figure 3: Likelihood contours in the $h-\Omega_M$ plane, derived from measurements of the BAO observed in the SDSS combined with constraints from other cosmological data. The intensities are separated by $-2\ln{\cal L}=2.3,\,6.0,\,9.2$, corresponding to two-parameter confidence of 68%, 95% and 99% for a Gaussian distribution. The blue shaded region shows the constraints for flat $\Lambda$ cosmologies combining the SDSS BAO data with a low redshift constraint on $h=0.72\pm0.08$ for flat $\Lambda$-cosmologies. The green region shows the combination of the SDSS constraint with the 3-year WMAP constraints on $\Omega_M^{0.275}h$ and $\Omega_bh^2$, again for flat $\Lambda$-cosmologies. The overlaid red contours were calculated by instead combining with a constraint on $\Omega_Mh^2$ from the peak heights in the CMB together with the constraint on $\Omega_bh^2$. This relaxes the assumption of a flat $\Lambda$-cosmology, by removing the dependence on the distance to the last scattering surface. There is still a dependence on the comoving distance-redshift relation over the survey, but observations of type Ia supernovae constrain this to be close to that expected for a flat $\Lambda$-cosmology. The degeneracies in the $h-\Omega_M$ plane induced by different cosmological observations are discussed at length in tegmark06.