Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies

TL;DR

This paper reports a significant detection of the baryon acoustic peak in the large-scale correlation function of SDSS Luminous Red Galaxies, confirming the imprint of early-universe sound waves on late-time structure and providing a geometric standard ruler. By modeling selection functions, applying non-linear and redshift-space corrections, and validating with extensive mock catalogs, the authors extract the acoustic scale and constrain $\Omega_m h^2$, distance measures $D_V(0.35)$, and the relative distance to the CMB epoch, all in agreement with CMB-based cosmology. The results yield strong evidence for dark energy and tight limits on spatial curvature, while illustrating how low-redshift acoustic measurements complement CMB data in constraining the cosmological model. Overall, the work demonstrates the power of large-volume galaxy surveys to test fundamental cosmology and to chart the expansion history of the universe through standard rulers.

Abstract

We present the large-scale correlation function measured from a spectroscopic sample of 46,748 luminous red galaxies from the Sloan Digital Sky Survey. The survey region covers 0.72 h^{-3} Gpc^3 over 3816 square degrees and 0.16<z<0.47, making it the best sample yet for the study of large-scale structure. We find a well-detected peak in the correlation function at 100h^{-1} Mpc separation that is an excellent match to the predicted shape and location of the imprint of the recombination-epoch acoustic oscillations on the low-redshift clustering of matter. This detection demonstrates the linear growth of structure by gravitational instability between z=1000 and the present and confirms a firm prediction of the standard cosmological theory. The acoustic peak provides a standard ruler by which we can measure the ratio of the distances to z=0.35 and z=1089 to 4% fractional accuracy and the absolute distance to z=0.35 to 5% accuracy. From the overall shape of the correlation function, we measure the matter density Omega_mh^2 to 8% and find agreement with the value from cosmic microwave background (CMB) anisotropies. Independent of the constraints provided by the CMB acoustic scale, we find Omega_m = 0.273 +- 0.025 + 0.123 (1+w_0) + 0.137 Omega_K. Including the CMB acoustic scale, we find that the spatial curvature is Omega_K=-0.010+-0.009 if the dark energy is a cosmological constant. More generally, our results provide a measurement of cosmological distance, and hence an argument for dark energy, based on a geometric method with the same simple physics as the microwave background anisotropies. The standard cosmological model convincingly passes these new and robust tests of its fundamental properties.

Figures (12)

• Figure 1: The effective volume (eq. [\ref{['eq:Veff']}]) as a function of wavenumber for various large redshift surveys. The effective volume is a rough guide to the performance of a survey (errors scaling as $V_{\rm eff}^{-1/2}$) but should not be trusted to better than 30%. To facilitate comparison, we have assumed 3816 square degrees for the SDSS Main sample, the same area as the SDSS LRG sample presented in this paper and similar to the area in Data Release 3. This is about 50% larger than the sample analyzed in Teg03a, which would be similar to the curve for the full 2dF Galaxy Redshift Survey Col03. We have neglected the potential gains on very large scales from the 99 outrigger fields of the 2dFGRS. The other surveys are the MX survey of clusters Mil01a, the PSCz survey of galaxies Sut99, and the 2QZ survey of quasars Cro04a. The SDSS DR3 quasar survey Sch05 is similar in effective volume to the 2QZ. For the amplitude of $P(k)$, we have used $\sigma_8=1$ for 2QZ and PSCz and 3.6 for the MX survey. We used $\sigma_8=1.8$ for SDSS LRG, SDSS Main, and the 2dFGRS; For the latter two, this value represents the amplitude of clustering of the luminous galaxies at the surveys' edge; at lower redshift, the number density is so high that the choice of $\sigma_8$ is irrelevant. Reducing SDSS Main or 2dFGRS to $\sigma_8=1$, the value typical of normal galaxies, decreases their $V_{\rm eff}$ by 30%.
• Figure 2: The large-scale redshift-space correlation function of the SDSS LRG sample. The error bars are from the diagonal elements of the mock-catalog covariance matrix; however, the points are correlated. Note that the vertical axis mixes logarithmic and linear scalings. The inset shows an expanded view with a linear vertical axis. The models are $\Omega_mh^2=0.12$ (top, green), 0.13 (red), and 0.14 (bottom with peak, blue), all with $\Omega_bh^2=0.024$ and $n=0.98$ and with a mild non-linear prescription folded in. The magenta line shows a pure CDM model ($\Omega_mh^2=0.105$), which lacks the acoustic peak. It is interesting to note that although the data appears higher than the models, the covariance between the points is soft as regards overall shifts in $\xi(s)$. Subtracting 0.002 from $\xi(s)$ at all scales makes the plot look cosmetically perfect, but changes the best-fit $\chi^2$ by only 1.3. The bump at $100h^{-1}{\rm\,Mpc}$ scale, on the other hand, is statistically significant.
• Figure 3: As Figure \ref{['fig:xi']}, but plotting the correlation function times $s^2$. This shows the variation of the peak at $20h^{-1}{\rm\,Mpc}$ scales that is controlled by the redshift of equality (and hence by $\Omega_mh^2$). Varying $\Omega_mh^2$ alters the amount of large-to-small scale correlation, but boosting the large-scale correlations too much causes an inconsistency at $30h^{-1}{\rm\,Mpc}$. The pure CDM model (magenta) is actually close to the best-fit due to the data points on intermediate scales.
• Figure 4: The correlation function for two different redshift slices, $0.16<z<0.36$ (filled squares, black) and $0.36<z<0.47$ (open squares, red). The latter is somewhat noisier, but the two are quite similar and both show evidence for the acoustic peak. Note that the vertical axis mixes logarithmic and linear scalings.
• Figure 5: Scale-dependent corrections derived from 51 N-body simulations, each $512h^{-1}{\rm\,Mpc}$ comoving with $256^3$ particles Seo04. The crosses show the ratio between the non-linear matter correlation function and the linear correlation function; the dashed line is the model we use from Smi03. The solid points are the ratio between the biased correlation function (using a simple halo mass cut) to the non-linear matter correlation function. The open squares are the ratio of the biased redshift-space correlation function to the biased real-space correlation function, after removing the large-scale asymptotic value Kai87, which we simply fold into the correlation amplitude parameter. The open triangles show the product of these two effects, and the solid line is our fit to this product. These corrections are of order 10% at $10h^{-1}{\rm\,Mpc}$ separations and decrease quickly on larger scales. In addition to these corrections, we mimic the erasure of the small-scale acoustic oscillations in the power spectrum by using a smoothed cross-over at $k=0.14h{\rm\,Mpc}^{-1}$ between the CMBfast linear power spectrum and the no-wiggle form from Eisenstein & Hu (1998).