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Register a new userClustering of Luminous Red Galaxies III: Detection of the Baryon Acoustic Peak in the 3-point Correlation Function
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We present the 3-point function xi_3 and Q_3=xi_3/xi_2^2 for a spectroscopic sample of luminous red galaxies (LRG) from SDSS DR6 & DR7. We find a strong (S/N$>$6) detection of $Q_3$ on scales of 55-125 Mpc/h, with a well defined peak around 105 Mpc/h in all xi_2, xi_3 and Q_3, in excellent agreement with the predicted shape and location of the imprint of the baryon acoustic oscillations (BAO). We use very large simulations to asses and test the significance of our measurement. Models without the BAO peak are ruled out by the $Q_3$ data with 99% confidence. Our measurements show the expected shape for Q_3 as a function of the triangular configuration. This provides a first direct measurement of the non-linear mode coupling coefficients of density and velocity fluctuations which, on these large scales, are independent of cosmic time, the amplitude of fluctuations or cosmological parameters. The location of the BAO peak in the data indicates Omega_m =0.28 pm 0.05 and Omega_B=0.079 pm 0.025 (h=0.70) after marginalization over spectral index (n_s=0.8-1.2) linear b_1 and quadratic c_2 bias,which are found to be in the range: b_1=1.7-2.2 and c_2=0.75-3.55. The data allows a hierarchical contribution from primordial non-Gaussianities in the range Q_3=0.55-3.35. These constraints are independent and complementary to the ones that can be obtained using the 2-point function, which are presented in a separate paper. This is the first detection of the shape of $Q_3$ on BAO scales, but our errors are shot-noise dominated and the SDSS volume is still relatively small, so there is ample room for future improvement in this type of measurements.
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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.
A new determination of the sound horizon scale in angular coordinates is presented. It makes use of ~ 0.6 x 10^6 Luminous Red Galaxies, selected from the Sloan Digital Sky Survey imaging data, with photometric redshifts. The analysis covers a redshift interval that goes from z=0.5 to z=0.6. We find evidence of the Baryon Acoustic Oscillations (BAO) signal at the ~ 2.3 sigma confidence level, with a value of theta_{BAO} (z=0.55) = (3.90 pm 0.38) degrees, including systematic errors. To our understanding, this is the first direct measurement of the angular BAO scale in the galaxy distribution, and it is in agreement with previous BAO measurements. We also show how radial determinations of the BAO scale can break the degeneracy in the measurement of cosmological parameters when they are combined with BAO angular measurements. The result is also in good agreement with the WMAP7 best-fit cosmology. We obtain a value of w_0 = -1.03 pm 0.16 for the equation of state parameter of the dark energy, Omega_M = 0.26 pm 0.04 for the matter density, when the other parameters are fixed. We have also tested the sensitivity of current BAO measurements to a time varying dark energy equation of state, finding w_a = 0.06 pm 0.22 if we fix all the other parameters to the WMAP7 best-fit cosmology.
We present baryon acoustic oscillation (BAO) scale measurements determined from the clustering of 1.2 million massive galaxies with redshifts 0.2 < z < 0.75 distributed over 9300 square degrees, as quantified by their redshift-space correlation function. In order to facilitate these measurements, we define, describe, and motivate the selection function for galaxies in the final data release (DR12) of the SDSS III Baryon Oscillation Spectroscopic Survey (BOSS). This includes the observational footprint, masks for image quality and Galactic extinction, and weights to account for density relationships intrinsic to the imaging and spectroscopic portions of the survey. We simulate the observed systematic trends in mock galaxy samples and demonstrate that they impart no bias on baryon acoustic oscillation (BAO) scale measurements and have a minor impact on the recovered statistical uncertainty. We measure transverse and radial BAO distance measurements in 0.2 < z < 0.5, 0.5 < z < 0.75, and (overlapping) 0.4 < z < 0.6 redshift bins. In each redshift bin, we obtain a precision that is 2.7 per cent or better on the radial distance and 1.6 per cent or better on the transverse distance. The combination of the redshift bins represents 1.8 per cent precision on the radial distance and 1.1 per cent precision on the transverse distance. This paper is part of a set that analyses the final galaxy clustering dataset from BOSS. The measurements and likelihoods presented here are combined with others in Alam et al. (2016) to produce the final cosmological constraints from BOSS.
We present distance scale measurements from the baryon acoustic oscillation signal in the CMASS and LOWZ samples from the Data Release 12 of the Baryon Oscillation Spectroscopic Survey (BOSS). The total volume probed is 14.5 Gpc$^3$, a 10 per cent increment from Data Release 11. From an analysis of the spherically averaged correlation function, we infer a distance to $z=0.57$ of $D_V(z)r^{rm fid}_{rm d}/r_ {rm d}=2028pm21$ Mpc and a distance to $z=0.32$ of $D_V(z)r^{rm fid}_{rm d}/r_{rm d}=1264pm22$ Mpc assuming a cosmology in which $r^{rm fid}_{rm d}=147.10$ Mpc. From the anisotropic analysis, we find an angular diameter distance to $z=0.57$ of $D_{rm A}(z)r^{rm fid}_{rm d}/r_{rm d}=1401pm21$ Mpc and a distance to $z=0.32$ of $981pm20$ Mpc, a 1.5 per cent and 2.0 per cent measurement respectively. The Hubble parameter at $z=0.57$ is $H(z)r_{rm d}/r^{rm fid}_{rm d}=100.3pm3.7$ km s$^{-1}$ Mpc$^{-1}$ and its value at $z=0.32$ is $79.2pm5.6$ km s$^{-1}$ Mpc$^{-1}$, a 3.7 per cent and 7.1 per cent measurement respectively. These cosmic distance scale constraints are in excellent agreement with a $Lambda$CDM model with cosmological parameters released by the recent Planck 2015 results.
Third-order statistics of the cosmic density field provides a powerful cosmological probe containing synergistic information to the more commonly explored second-order statistics. Here, we exploit a spectroscopic catalog of 72,563 clusters of galaxies extracted from the Sloan Digital Sky Survey, providing the first detection of the baryon acoustic oscillations (BAO) peak in the three-point correlation function (3PCF) of galaxy clusters. We measure and analyze both the connected and the reduced 3PCF of SDSS clusters from intermediate ($rsim10$ Mpc/h) up to large ($rsim140$ Mpc/h) scales, exploring a variety of different configurations. From the analysis of reduced 3PCF at intermediate scales, in combination with the analysis of the two-point correlation function, we constrain both the cluster linear and non-linear bias parameters, $b_1=2.75pm0.03$ and $b_2=1.2pm0.5$. We analyze the measurements of the 3PCF at larger scales, comparing them with theoretical models. The data show clear evidence of the BAO peak in different configurations, which appears more visible in the reduced 3PCF rather than in the connected one. From the comparison between theoretical models considering or not the BAO peak, we obtain a quantitative estimate of this evidence, with a $Delta chi^2$ between 2 and 75, depending on the considered configuration. Finally, we set up a generic framework to estimate the expected signal-to-noise ratio of the BAO peak in the 3PCF exploring different possible definitions, that can be used to forecast the most favorable configurations to be explored also in different future surveys, and applied it to the case of the Euclid mission.
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