Cosmological constraints from the SDSS luminous red galaxies

Monthly Notices of …, 2010

We present the power spectrum of the reconstructed halo density field derived from a sample of Luminous Red Galaxies (LRGs) from the Sloan Digital Sky Survey Seventh Data Release (DR7). The halo power spectrum has a direct connection to the underlying dark matter power for k 0.2 h Mpc −1 , well into the quasi-linear regime. This enables us to use a factor of ∼ 8 more modes in the cosmological analysis than an analysis with k max = 0.1 h Mpc −1 , as was adopted in the SDSS team analysis of the DR4 LRG sample . The observed halo power spectrum for 0.02 < k < 0.2 h Mpc −1 is well-fit by our model: χ 2 = 39.6 for 40 degrees of freedom for the best-fitting ΛCDM model. We find Ω m h 2 (n s /0.96) 0.13 = 0.141 +0.009 −0.012 for a power law primordial power spectrum with spectral index n s and Ω b h 2 = 0.02265 fixed, consistent with CMB measurements. The halo power spectrum also constrains the ratio of the comoving sound horizon at the baryon-drag epoch to an effective distance to z = 0.35: r s /D V (0.35) = 0.1097 +0.0039 −0.0042 . Combining the halo power spectrum measurement with the WMAP 5 year results, for the flat ΛCDM model we find ⋆ c 0000 RAS 2 Beth A. Reid et al.

Monthly Notices of the Royal Astronomical Society, 2019

Likelihood fitting to two-point clustering statistics made from galaxy surveys usually assumes a multivariate normal distribution for the measurements, with justification based on the central limit theorem given the large number of overdensity modes. However, this assumption cannot hold on the largest scales where the number of modes is low. Whilst more accurate distributions have previously been developed in idealized cases, we derive a procedure suitable for analysing measured monopole power spectra with window effects, stochastic shot noise and the dependence of the covariance matrix on the model being fitted all taken into account. A data transformation is proposed to give an approximately Gaussian likelihood, with a variance-correlation decomposition of the covariance matrix to account for its cosmological dependence. By comparing with the modified-t likelihood derived under the usual normality assumption, we find in numerical tests that our new procedure gives more accurate constraints on the local non-Gaussianity parameter f NL , which is sensitive to the large-scale power. A simple data analysis pipeline is provided for straightforward application of this new approach in preparation for forthcoming large galaxy surveys such as DESI and Euclid.

Precision measurements of the galaxy power spectrum P (k) require a data analysis pipeline that is both fast enough to be computationally feasible and accurate enough to take full advantage of high-quality data. We present a rigorous discussion of different methods of power spectrum estimation, with emphasis on the traditional Fourier method, and linear (Karhunen-Loève; KL), and quadratic data compression schemes, showing in what approximations they give the same result. To improve speed, we show how many of the advantages of KL data compression and power spectrum estimation may be achieved with a computationally faster quadratic method. To improve accuracy, we derive analytic expressions for handling the integral constraint, since it is crucial that finite volume effects are accurately corrected for on scales comparable to the depth of the survey. We also show that for the KL and quadratic techniques, multiple constraints can be included via simple matrix operations, thereby rendering the results less sensitive to galactic extinction and mis-estimates of the radial selection function. We present a data analysis pipeline that we argue does justice to the increases in both quality and quantity of data that upcoming redshift surveys will provide. It uses three analysis techniques in conjunction: a traditional Fourier approach on small scales, a pixelized quadratic matrix method on large scales and a pixelized KL eigenmode analysis to probe anisotropic effects such as redshift-space distortions.

Monthly Notices of the Royal Astronomical Society, 2011

We present the power spectrum of the reconstructed halo density field derived from a sample of Luminous Red Galaxies (LRGs) from the Sloan Digital Sky Survey Seventh Data Release (DR7). The halo power spectrum has a direct connection to the underlying dark matter power for k 0.2 h Mpc −1 , well into the quasi-linear regime. This enables us to use a factor of ∼ 8 more modes in the cosmological analysis than an analysis with k max = 0.1 h Mpc −1 , as was adopted in the SDSS team analysis of the DR4 LRG sample . The observed halo power spectrum for 0.02 < k < 0.2 h Mpc −1 is well-fit by our model: χ 2 = 39.6 for 40 degrees of freedom for the best-fitting ΛCDM model. We find Ω m h 2 (n s /0.96) 0.13 = 0.141 +0.009 −0.012 for a power law primordial power spectrum with spectral index n s and Ω b h 2 = 0.02265 fixed, consistent with CMB measurements. The halo power spectrum also constrains the ratio of the comoving sound horizon at the baryon-drag epoch to an effective distance to z = 0.35: r s /D V (0.35) = 0.1097 +0.0039 −0.0042 . Combining the halo power spectrum measurement with the WMAP 5 year results, for the flat ΛCDM model we find ⋆ c 0000 RAS 2 Beth A. Reid et al.

We present estimates of cosmological parameters from the application of the Karhunen-Loève transform to the analysis of the 3D power spectrum of density fluctuations using Sloan Digital Sky Survey galaxy redshifts. We use Ω m h and f b = Ω b /Ω m to describe the shape of the power spectrum, σ L 8g for the (linearly extrapolated) normalization, and β to parametrize linear theory redshift space distortions. On scales k 0.16hMpc −1 , our maximum likelihood values are Ω m h = 0.264 ± 0.043, f b = 0.286 ± 0.065, σ L 8g = 0.966±0.048, and β = 0.45±0.12. When we take a prior on Ω b from WMAP, we find Ω m h = 0.207±0.030, which is in excellent agreement with WMAP and 2dF. This indicates that we have reasonably measured the gross shape of the power spectrum but we have difficulty breaking the degeneracy between Ω m h and f b because the baryon oscillations are not resolved in the current spectroscopic survey window function.

The Astrophysical Journal, 2007

We present a Fourier analysis of the clustering of galaxies in the combined Main galaxy and Luminous Red Galaxy (LRG) Sloan Digital Sky Survey (SDSS) Data Release 5 (DR5) sample. The aim of our analysis is to consider how well we can measure the cosmological matter density using the signature of the horizon at matter-radiation equality embedded in the large-scale power spectrum. The new data constrains the power spectrum on scales 100-600 h −1 Mpc with significantly higher precision than previous analyses of just the SDSS Main galaxies, due to our larger sample and the inclusion of the LRGs. This improvement means that we can now reveal a discrepancy between the shape of the measured power and linear CDM models on scales 0.01 < k < 0.15 h Mpc −1 , with linear model fits favouring a lower matter density (Ω M = 0.22 ± 0.04) on scales 0.01 < k < 0.06 h Mpc −1 and a higher matter density (Ω M = 0.32 ± 0.01) when smaller scales are included, assuming a flat ΛCDM model with h = 0.73 and n s = 0.96. The lower matter density favoured by fitting our SDSS data for 0.01 < k < 0.06 h Mpc −1 is a better match to the best-fit WMAP 3-year cosmological model, and to results from the positions of the baryon oscillations observed in the SDSS DR5 power spectrum. This discrepancy could be explained by scale-dependent bias and, by analysing subsamples of galaxies, we find that the ratio of small-scale to large-scale power increases with galaxy luminosity, so all of the SDSS galaxies cannot trace the same power spectrum shape over 0.01 < k < 0.2 h Mpc −1 . However, the data are insufficient to clearly show a luminosity-dependent change in the largest scale at which a significant increase in clustering is observed, although they do not rule out such an effect. Significant scale-dependent galaxy bias on large-scales, which changes with the r-band luminosity of the galaxies, could potentially explain differences in our Ω M estimates and differences previously observed between 2dFGRS and SDSS power spectra and the resulting parameter constraints.

The Astrophysical Journal, 2012

The Sloan Digital Sky Survey (SDSS) surveyed 14,555 square degrees, and delivered over a trillion pixels of imaging data. We present a study of galaxy clustering using 900,000 luminous galaxies with photometric redshifts, spanning between z = 0.45 and z = 0.65, constructed from the SDSS using methods described in Ross et al. (2011). This data-set spans 11,000 square degrees and probes a volume of 3h −3 Gpc 3 , making it the largest volume ever used for galaxy clustering measurements. We describe in detail the construction of the survey window function and various systematics affecting our measurement. With such a large volume, high precision cosmological constraints can be obtained given a careful control and understanding of the observational systematics. We present a novel treatment of the observational systematics and its applications to the clustering signals from the data set. In this paper, we measure the angular clustering using an optimal quadratic estimator at 4 redshift slices with an accuracy of ∼ 15% with bin size of δ l = 10 on scales of the Baryon Acoustic Oscillations (BAO) (at ∼ 40 − 400). We also apply corrections to the power-spectra due to systematics, and derive cosmological constraints using the full-shape of the power-spectra. For a flat ΛCDM model, when combined with Cosmic Microwave Background Wilkinson Microwave Anisotropy Probe 7 (WMAP7) and H 0 constraints from using 600 Cepheids observed by Wide Feild Camera 3 (WFC3) (HST) , we find Ω Λ = 0.73 ± 0.019 and H 0 to be 70.5 ± 1.6 s −1 Mpc −1 km. For an open ΛCDM model, when combined with WMAP7 + HST, we find Ω K = 0.0035 ± 0.0054, improved over WMAP7+HST alone by 40%. For a wCDM model, when combined with WMAP7+HST+SN, we find w = −1.071 ± 0.078, and H 0 to be 71.3 ± 1.7 s −1 Mpc −1 km, which is competitive with the latest large scale structure constraints from large spectroscopic surveys such as SDSS Data Release 7 (DR7) (Reid et al. 2010, Percival et al. 2010, Montesano et al. 2011) and WiggleZ (Blake et al. 2011). We also find that systematic-corrected power-spectra gives consistent constraints on cosmological models when compared with pre-systematic correction power-spectra in the angular scales of interest. The SDSS-III Data Release 8 (SDSS-III DR8) Angular Clustering Data allows a wide range of investigations into the cosmological model, cosmic expansion (via BAO), Gaussianity of initial conditions and neutrino masses. Here, we refer to our companion papers (Seo et al. 2011, de Putter et al. 2011) for further investigations using the clustering data. Our calculation of survey selection function, systematics maps, likelihood function for COSMOMC package will be released at

We compute the angular power spectrum C from 1.5 million galaxies in early SDSS data on large angular scales, ∼ < 600. The data set covers about 160 square degrees, with a characteristic depth of order 1h −1 Gpc in the faintest (21 < r < 22) of our four magnitude bins. Cosmological interpretations of these results are presented in a companion paper by Dodelson et al. (2001). The data in all four magnitude bins are consistent with a simple flat "concordance" model with nonlinear evolution and linear bias factors of order unity. Nonlinear evolution is particularly evident for the brightest galaxies. A series of tests suggest that systematic errors related to seeing, reddening, etc., are negligible, which bodes well for the sixtyfold larger sample that the SDSS is currently collecting. Uncorrelated error bars and well-behaved window functions make our measurements a convenient starting point for cosmological model fitting.