Homotopy Perturbation Method and the Stagnation Point Flow

The laminar steady flow of an incompressible, viscous fluid near a stagnation point has been computed using the homotopy perturbation method (HPM). Both the cases, (i) two-dimensional flow and (ii) axisymmetric flow, have been considered. A sequence of successive approximations has been obtained in the solution, and the convergence of the sequence is achieved by using the Padé approximants. It is found that there is a complete agreement between the results obtained by the HPM and the exact numerical solution

Beyond Λ\LambdaCDM constraints from the full shape clustering measurements from BOSS and eBOSS

We analyse the full shape of anisotropic clustering measurements from the extended Baryon Oscillation Spectroscopic survey (eBOSS) quasar sample together with the combined galaxy sample from the Baryon Oscillation Spectroscopic Survey (BOSS). We obtain constraints on the cosmological parameters independent of the Hubble parameter $h$ for the extensions of the $\Lambda$CDM models, focusing on cosmologies with free dark energy equation of state parameter $w$. We combine the clustering constraints with those from the latest CMB data from Planck to obtain joint constraints for these cosmologies for $w$ and the additional extension parameters - its time evolution $w_{\rm{a}}$, the physical curvature density $\omega_{K}$ and the neutrino mass sum $\sum m_{\nu}$. Our joint constraints are consistent with flat $\Lambda$CDM cosmological model within 68\% confidence limits. We demonstrate that the Planck data are able to place tight constraints on the clustering amplitude today, $\sigma_{12}$, in cosmologies with varying $w$ and present the first constraints for the clustering amplitude for such cosmologies, which is found to be slightly higher than the $\Lambda$CDM value. Additionally, we show that when we vary $w$ and allow for non-flat cosmologies and the physical curvature density is used, Planck prefers a curved universe at $4\sigma$ significance, which is $\sim2\sigma$ higher than when using the relative curvature density $\Omega_{\rm{K}}$. Finally, when $w$ is varied freely, clustering provides only a modest improvement (of 0.021 eV) on the upper limit of $\sum m_{\nu}$.Comment: 12 pages, 6 figures, submitted to MNRA

The clustering of Galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey : including covariance matrix errors

JP acknowledges support from the UK Science & Technology Facilities Council (STFC) through the consolidated grant ST/K0090X/1 and from the European Research Council through the ‘Starting Independent Research’ grant 202686, MDEPUGS. AGS acknowledges support from the Trans-regional Collaborative Research Centre TR33 ‘The Dark Universe’ of the German Research Foundation (DFG).We present improved methodology for including covariance matrices in the error budget of Baryon Oscillation Spectroscopic Survey (BOSS) galaxy clustering measurements, revisiting Data Release 9 (DR9) analyses, and describing a method that is used in DR10/11 analyses presented in companion papers. The precise analysis method adopted is becoming increasingly important, due to the precision that BOSS can now reach: even using as many as 600 mock catalogues to estimate covariance of two-point clustering measurements can still lead to an increase in the errors of ∼20 per cent, depending on how the cosmological parameters of interest are measured. In this paper, we extend previous work on this contribution to the error budget, deriving formulae for errors measured by integrating over the likelihood, and to the distribution of recovered best-fitting parameters fitting the simulations also used to estimate the covariance matrix. Both are situations that previous analyses of BOSS have considered. We apply the formulae derived to baryon acoustic oscillation (BAO) and redshift-space distortion (RSD) measurements from BOSS in our companion papers. To further aid these analyses, we consider the optimum number of bins to use for two-point measurements using the monopole power spectrum or correlation function for BAO, and the monopole and quadrupole moments of the correlation function for anisotropic-BAO and RSD measurements.Publisher PDFPeer reviewe

Devonian Rise in Atmospheric Oxygen Correlated to the Radiations of Terrestrial Plants and Large Predatory Fish

The evolution of Earth’s biota is intimately linked to the oxygenation of the oceans and atmosphere. We use the isotopic composition and concentration of molybdenum (Mo) in sedimentary rocks to explore this relationship. Our results indicate two episodes of global ocean oxygenation. The first coincides with the emergence of the Ediacaran fauna, including large, motile bilaterian animals, ca. 550-560 million year ago (Ma), reinforcing previous geochemical indications that Earth surface oxygenation facilitated this radiation. The second, perhaps larger, oxygenation took place around 400 Ma, well after the initial rise of animals and, therefore, suggesting that early metazoans evolved in a relatively low oxygen environment. This later oxygenation correlates with the diversification of vascular plants, which likely contributed to increased oxygenation through the enhanced burial of organic carbon in sediments. It also correlates with a pronounced radiation of large predatory fish, animals with high oxygen demand. We thereby couple the redox history of the atmosphere and oceans to major events in animal evolution.Earth and Planetary SciencesOrganismic and Evolutionary Biolog

The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey : cosmological implications of the full shape of the clustering wedges in the data release 10 and 11 galaxy samples

We explore the cosmological implications of the angle-averaged correlation function, ξ(s), and the clustering wedges, ξ⊥(s) and ξ∥(s), of the LOWZ and CMASS galaxy samples from Data Releases 10 and 11 of the Sloan Digital Sky Survey III (SDSS-III) Baryon Oscillation Spectroscopic Survey. Our results show no significant evidence for a deviation from the standard Λ cold dark matter model. The combination of the information from our clustering measurements with recent data from the cosmic microwave background is sufficient to constrain the curvature of the Universe to Ωk = 0.0010 ± 0.0029, the total neutrino mass to ∑mν < 0.23 eV (95 per cent confidence level), the effective number of relativistic species to Neff = 3.31 ± 0.27 and the dark energy equation of state to wDE = −1.051 ± 0.076. These limits are further improved by adding information from Type Ia supernovae and baryon acoustic oscillations from other samples. In particular, this data set combination is completely consistent with a time-independent dark energy equation of state, in which case we find wDE = −1.024 ± 0.052. We explore the constraints on the growth rate of cosmic structures assuming f(z) = Ωm(z)γ and obtain γ = 0.69 ± 0.15, consistent with the predictions of general relativity of γ = 0.55.Publisher PDFPeer reviewe

Ameliorating Systematic Uncertainties in the Angular Clustering of Galaxies: A Study using SDSS-III

We investigate the effects of potential sources of systematic error on the angular and photometric redshift, z_phot, distributions of a sample of redshift 0.4 < z < 0.7 massive galaxies whose selection matches that of the Baryon Oscillation Spectroscopic Survey (BOSS) constant mass sample. Utilizing over 112,778 BOSS spectra as a training sample, we produce a photometric redshift catalog for the galaxies in the SDSS DR8 imaging area that, after masking, covers nearly one quarter of the sky (9,913 square degrees). We investigate fluctuations in the number density of objects in this sample as a function of Galactic extinction, seeing, stellar density, sky background, airmass, photometric offset, and North/South Galactic hemisphere. We find that the presence of stars of comparable magnitudes to our galaxies (which are not traditionally masked) effectively remove area. Failing to correct for such stars can produce systematic errors on the measured angular auto-correlation function, w, that are larger than its statistical uncertainty. We describe how one can effectively mask for the presence of the stars, without removing any galaxies from the sample, and minimize the systematic error. Additionally, we apply two separate methods that can be used to correct the systematic errors imparted by any parameter that can be turned into a map on the sky. We find that failing to properly account for varying sky background introduces a systematic error on w. We measure w, in four z_phot slices of width 0.05 between 0.45 < z_phot < 0.65 and find that the measurements, after correcting for the systematic effects of stars and sky background, are generally consistent with a generic LambdaCDM model, at scales up to 60 degrees. At scales greater than 3 degrees and z_phot > 0.5, the magnitude of the corrections we apply are greater than the statistical uncertainty in w.Comment: Accepted by MNRA

The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: measuring structure growth using passive galaxies

We explore the benefits of using a passively evolving population of galaxies to measure the evolution of the rate of structure growth between z=0.25 and z=0.65 by combining data from the SDSS-I/II and SDSS-III surveys. The large-scale linear bias of a population of dynamically passive galaxies, which we select from both surveys, is easily modeled. Knowing the bias evolution breaks degeneracies inherent to other methodologies, and decreases the uncertainty in measurements of the rate of structure growth and the normalization of the galaxy power-spectrum by up to a factor of two. If we translate our measurements into a constraint on sigma_8(z=0) assuming a concordance cosmological model and General Relativity (GR), we find that using a bias model improves our uncertainty by a factor of nearly 1.5. Our results are consistent with a flat Lambda Cold Dark Matter model and with GR.Comment: Accepted for publication in MNRAS (clarifications added, results and conclusions unchanged

The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey : measuring DA and H at z = 0.57 from the baryon acoustic peak in the Data Release 9 spectroscopic Galaxy sample

We present measurements of the angular diameter distance to and Hubble parameter at z = 0.57 from the measurement of the baryon acoustic peak in the correlation of galaxies from the Sloan Digital Sky Survey III Baryon Oscillation Spectroscopic Survey. Our analysis is based on a sample from Data Release 9 of 264 283 galaxies over 3275 square degrees in the redshift range 0.43 < z < 0.70. We use two different methods to provide robust measurement of the acoustic peak position across and along the line of sight in order to measure the cosmological distance scale. We find DA(0.57) = 1408 ± 45 Mpc and H(0.57) = 92.9 ± 7.8 km s−1 Mpc−1 for our fiducial value of the sound horizon. These results from the anisotropic fitting are fully consistent with the analysis of the spherically averaged acoustic peak position presented in Anderson et al. Our distance measurements are a close match to the predictions of the standard cosmological model featuring a cosmological constant and zero spatial curvature.Publisher PDFPeer reviewe