We introduce a method to constrain general cosmological models using Baryon Acoustic Oscillation (BAO) distance measurements from galaxy samples covering different redshift ranges, and apply this ...method to analyse samples drawn from the Sloan Digital Sky Survey (SDSS) and 2dF Galaxy Redshift Survey (2dFGRS). BAOs are detected in the clustering of the combined 2dFGRS and SDSS main galaxy samples, and measure the distance–redshift relation at z= 0.2. BAOs in the clustering of the SDSS luminous red galaxies measure the distance–redshift relation at z= 0.35. The observed scales of the BAOs calculated from these samples and from the combined sample are jointly analysed using estimates of the correlated errors, to constrain the form of the distance measure DV(z) ≡(1 +z)2D2Acz/H(z)1/3. Here DA is the angular diameter distance, and H(z) is the Hubble parameter. This gives rs/DV(0.2) = 0.1980 ± 0.0058 and rs/DV(0.35) = 0.1094 ± 0.0033 (1σ errors), with a correlation coefficient of 0.39, where rs is the comoving sound horizon scale at recombination. Matching the BAOs to have the same measured scale at all redshifts then gives DV(0.35)/DV(0.2) = 1.812 ± 0.060. The recovered ratio is roughly consistent with that predicted by the higher redshift Supernova Legacy Survey (SNLS) supernova data for Λ cold dark matter cosmologies, but does require slightly stronger cosmological acceleration at a low redshift. If we force the cosmological model to be flat with constant w, then we find Ωm= 0.249 ± 0.018 and w=−1.004 ± 0.089 after combining with the SNLS data, and including the WMAP measurement of the apparent acoustic horizon angle in the cosmic microwave background.
We seek to improve estimates of the power spectrum covariance matrix from a limited number of simulations by employing a novel statistical technique known as shrinkage estimation. The shrinkage ...technique optimally combines an empirical estimate of the covariance with a model (the target) to minimize the total mean squared error compared to the true underlying covariance. We test this technique on N-body simulations and evaluate its performance by estimating cosmological parameters. Using a simple diagonal target, we show that the shrinkage estimator significantly outperforms both the empirical covariance and the target individually when using a small number of simulations. We find that reducing noise in the covariance estimate is essential for properly estimating the values of cosmological parameters as well as their confidence intervals. We extend our method to the jackknife covariance estimator and again find significant improvement, though simulations give better results. Even for thousands of simulations we still find evidence that our method improves estimation of the covariance matrix. Because our method is simple, requires negligible additional numerical effort, and produces superior results, we always advocate shrinkage estimation for the covariance of the power spectrum and other large-scale structure measurements when purely theoretical modelling of the covariance is insufficient.
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 and main samples, and also include the 2-degree Field Galaxy Redshift Survey data. In total, this sample comprises 893 319 galaxies over 9100 deg2. Baryon acoustic oscillations (BAO) 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 rs(zd)/DV(0.275) = 0.1390 ± 0.0037 (2.7 per cent accuracy), where rs(zd) is the comoving sound horizon at the baryon-drag epoch, DV(z) ≡(1 +z)2D2Acz/H(z)1/3, DA(z) is the angular diameter distance and H(z) is the Hubble parameter. We find an almost independent constraint on the ratio of distances DV(0.35)/DV(0.2) = 1.736 ± 0.065, which is consistent at the 1.1σ level with the best-fitting Λ cold dark matter model obtained when combining our z= 0.275 distance constraint with the Wilkinson Microwave Anisotropy Probe 5-year (WMAP5) 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 Ωbh2 and Ωc h2, and combining our BAO distance measurements with those from the Union supernova sample, places a tight constraint on Ωm= 0.286 ± 0.018 and H0= 68.2 ± 2.2 km s−1 Mpc−1 that is robust to allowing Ωk≠ 0 and w≠−1. This result is independent of the behaviour of dark energy at redshifts greater than those probed by the BAO and supernova measurements. Combining these data sets with the full WMAP5 likelihood constraints provides tight constraints on both Ωk=−0.006 ± 0.008 and w=−0.97 ± 0.10 for a constant dark energy equation of state.
We present a Fourier analysis of the clustering of galaxies in the combined main galaxy and LRG SDSS 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 constrain the power spectrum on scales 100-600 h super(-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 h Mpc super(-1) < k < 0.15 h Mpc super(-1), with linear model fits favoring a lower matter density ( sub(M)=0.22 c 0.04) on scales 0.01 h Mpc super(-1) < k < 0.06 h Mpc super(-1) and a higher matter density ( sub(M)= 0.32 c 0.01) when smaller scales are included, assuming a flat ACDM model with h = 0.73 and n sub(s) = 0.96. This discrepancy could be explained by scale-dependent bias, and by analyzing 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 h Mpc super(-1) 0.2h Mpc super(-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 sub(M) estimates and differences previously observed between 2dFGRS and SDSS power spectra and the resulting parameter constraints.
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 (SDSS) 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 kmax= 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 fitted by our model: χ2= 39.6 for 40 degrees of freedom for the best-fitting Λ cold dark matter (ΛCDM) model. We find Ωmh2(ns/0.96)1.2= 0.141+0.010−0.012 for a power-law primordial power spectrum with spectral index ns and Ωbh2= 0.022 65 fixed, consistent with cosmic microwave background 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: rs/DV(0.35) = 0.1097+0.0039−0.0042. Combining the halo power spectrum measurement with the Wilkinson Microwave Anisotropy Probe (WMAP) 5 year results, for the flat ΛCDM model we find Ωm= 0.289 ± 0.019 and H0= 69.4 ± 1.6 km s−1 Mpc−1. Allowing for massive neutrinos in ΛCDM, we find eV at the 95 per cent confidence level. If we instead consider the effective number of relativistic species Neff as a free parameter, we find Neff= 4.8+1.8−1.7. Combining also with the Kowalski et al. supernova sample, we find Ωtot= 1.011 ± 0.009 and w=−0.99 ± 0.11 for an open cosmology with constant dark energy equation of state w. The power spectrum and a module to calculate the likelihoods are publicly available at http://lambda.gsfc.nasa.gov/toolbox/lrgdr/.
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 analyze 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 (3.0 s 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 sub(M) = 0.256 super(+) sub(-) super(0) sub(0) super(.) sub(.) super(0) sub(0) super(2) sub(2) super(9) sub(4)(68% confidence interval) for a flat cosmology when marginalizing 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.
We present estimates of cosmological parameters from the application of the Karhunen-Loeve transform to the analysis of the three-dimensional power spectrum of density fluctuations using Sloan ...Digital Sky Survey galaxy redshifts. We use Omega sub(m)h and f sub(b) = Omega sub(b)/Omega sub(m) to describe the shape of the power spectrum, sigma super(L) sub(8g) for the (linearly extrapolated) normalization, and beta to parameterize linear theory redshift-space distortions. On scales k ~ 0.16 h Mpc super(-1), our maximum likelihood values are Omega sub(m)h = 0.264 plus or minus 0.043, f sub(b) = 0.286 plus or minus 0.065, sigma super(L) sub(8g) = 0.966 plus or minus 0.048, and beta = 0.45 plus or minus 0.12. When we take a prior on Omega sub(b) from the Wilkinson Microwave Anisotropy Probe (WMAP), we find Omega sub(m)h = 0.207 plus or minus 0.030, which is in excellent agreement with WMAP and the Two-Degree Field. This indicates that we have reasonably measured the gross shape of the power spectrum, but we have difficulty breaking the degeneracy between Omega sub(m)h and f sub(b), because the baryon oscillations are not resolved in the current spectroscopic survey window function.
We present the design and performance of the multi-object fiber spectrographs for the Sloan Digital Sky Survey (SDSS) and their upgrade for the Baryon Oscillation Spectroscopic Survey (BOSS). ...Originally commissioned in Fall 1999 on the 2.5 m aperture Sloan Telescope at Apache Point Observatory, the spectrographs produced more than 1.5 million spectra for the SDSS and SDSS-II surveys, enabling a wide variety of Galactic and extra-galactic science including the first observation of baryon acoustic oscillations in 2005. The spectrographs were upgraded in 2009 and are currently in use for BOSS, the flagship survey of the third-generation SDSS-III project. BOSS will measure redshifts of 1.35 million massive galaxies to redshift 0.7 and Ly alpha absorption of 160,000 high redshift quasars over 10,000 deg super(2) of sky, making percent level measurements of the absolute cosmic distance scale of the universe and placing tight constraints on the equation of state of dark energy. The twin multi-object fiber spectrographs utilize a simple optical layout with reflective collimators, gratings, all-refractive cameras, and state-of-the-art CCD detectors to produce hundreds of spectra simultaneously in two channels over a bandpass covering the near-ultraviolet to the near-infrared, with a resolving power R = lambda/FWHM ~ 2000. Building on proven heritage, the spectrographs were upgraded for BOSS with volume-phase holographic gratings and modern CCD detectors, improving the peak throughput by nearly a factor of two, extending the bandpass to cover 360 nm < lambda < 1000 nm, and increasing the number of fibers from 640 to 1000 per exposure. In this paper we describe the original SDSS spectrograph design and the upgrades implemented for BOSS, and document the predicted and measured performances.
Summary Background In the Global Burden of Disease Study 2013 (GBD 2013), knowledge about health and its determinants has been integrated into a comparable framework to inform health policy. Outputs ...of this analysis are relevant to current policy questions in England and elsewhere, particularly on health inequalities. We use GBD 2013 data on mortality and causes of death, and disease and injury incidence and prevalence to analyse the burden of disease and injury in England as a whole, in English regions, and within each English region by deprivation quintile. We also assess disease and injury burden in England attributable to potentially preventable risk factors. England and the English regions are compared with the remaining constituent countries of the UK and with comparable countries in the European Union (EU) and beyond. Methods We extracted data from the GBD 2013 to compare mortality, causes of death, years of life lost (YLLs), years lived with a disability (YLDs), and disability-adjusted life-years (DALYs) in England, the UK, and 18 other countries (the first 15 EU members apart from the UK and Australia, Canada, Norway, and the USA EU15+). We extended elements of the analysis to English regions, and subregional areas defined by deprivation quintile (deprivation areas). We used data split by the nine English regions (corresponding to the European boundaries of the Nomenclature for Territorial Statistics level 1 NUTS 1 regions), and by quintile groups within each English region according to deprivation, thereby making 45 regional deprivation areas. Deprivation quintiles were defined by area of residence ranked at national level by Index of Multiple Deprivation score, 2010. Burden due to various risk factors is described for England using new GBD methodology to estimate independent and overlapping attributable risk for five tiers of behavioural, metabolic, and environmental risk factors. We present results for 306 causes and 2337 sequelae, and 79 risks or risk clusters. Findings Between 1990 and 2013, life expectancy from birth in England increased by 5·4 years (95% uncertainty interval 5·0–5·8) from 75·9 years (75·9–76·0) to 81·3 years (80·9–81·7); gains were greater for men than for women. Rates of age-standardised YLLs reduced by 41·1% (38·3–43·6), whereas DALYs were reduced by 23·8% (20·9–27·1), and YLDs by 1·4% (0·1–2·8). For these measures, England ranked better than the UK and the EU15+ means. Between 1990 and 2013, the range in life expectancy among 45 regional deprivation areas remained 8·2 years for men and decreased from 7·2 years in 1990 to 6·9 years in 2013 for women. In 2013, the leading cause of YLLs was ischaemic heart disease, and the leading cause of DALYs was low back and neck pain. Known risk factors accounted for 39·6% (37·7–41·7) of DALYs; leading behavioural risk factors were suboptimal diet (10·8% 9·1–12·7) and tobacco (10·7% 9·4–12·0). Interpretation Health in England is improving although substantial opportunities exist for further reductions in the burden of preventable disease. The gap in mortality rates between men and women has reduced, but marked health inequalities between the least deprived and most deprived areas remain. Declines in mortality have not been matched by similar declines in morbidity, resulting in people living longer with diseases. Health policies must therefore address the causes of ill health as well as those of premature mortality. Systematic action locally and nationally is needed to reduce risk exposures, support healthy behaviours, alleviate the severity of chronic disabling disorders, and mitigate the effects of socioeconomic deprivation. Funding Bill & Melinda Gates Foundation and Public Health England.
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