arXiv subjects

Will J. Percival

Publications and source records attributed to Will J. Percival.

At least 217 records · Page 12Linked to original sources

arXiv2012

New Neutrino Mass Bounds from Sloan Digital Sky Survey III Data Release 8 Photometric Luminous Galaxies

We present neutrino mass bounds using 900,000 luminous galaxies with photometric redshifts measured from Sloan Digital Sky Survey III Data Release Eight (SDSS DR8). The galaxies have photometric redshifts between $z = 0.45$ and $z = 0.65$, and cover 10,000 square degrees and thus probe a volume of 3$h^{-3}$Gpc$^3$, enabling tight constraints to be derived on the amount of dark matter in the form of massive neutrinos. A new bound on the sum of neutrino masses $\sum m_ν< 0.26$ eV, at 95% confidence level (CL), is obtained after combining our sample of galaxies, which we call "CMASS", with WMAP 7 year Cosmic Microwave Background (CMB) data and the most recent measurement of the Hubble parameter from the Hubble Space Telescope (HST). This constraint is obtained with a conservative multipole range choice of $30 < \ell < 200$ in order to minimize non-linearities, and a free bias parameter in each of the four redshift bins. We study the impact of assuming this linear galaxy bias model using mock catalogs, and find that this model causes a small ($\sim 1-1.5 σ$) bias in $Ω_{\rm DM} h^2$. For this reason, we also quote neutrino bounds based on a conservative galaxy bias model containing additional, shot noise-like free parameters. In this conservative case, the bounds are significantly weakened, e.g. $\sum m_ν< 0.36$ eV (95% confidence level) for WMAP+HST+CMASS ($\ell_{\rm max}=200$). We also study the dependence of the neutrino bound on multipole range ($\ell_{\rm max}=150$ vs $\ell_{\rm max}=200$) and on which combination of data sets is included as a prior. The addition of supernova and/or Baryon Acoustic Oscillation data does not significantly improve the neutrino mass bound once the HST prior is included. [abridged]

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arXiv2011

Interpreting large-scale redshift-space distortion measurements

The simplest theory describing large-scale redshift-space distortions (RSD), based on linear theory and distant galaxies, depends on the growth of cosmological structure, suggesting that strong tests of General Relativity can be constructed from galaxy surveys. As data sets become larger and the expected constraints more precise, the extent to which the RSD follow the simple theory needs to be assessed in order that we do not introduce systematic errors into the tests by introducing inaccurate simplifying assumptions. We study the impact of the sample geometry, non-linear processes, and biases induced by our lack of understanding of the radial galaxy distribution on RSD measurements. Using LasDamas simulations of the Sloan Digital Sky Survey II (SDSS-II) Luminous Red Galaxy (LRG) data, these effects are shown to be important at the level of 20 per cent. Including them, we can accurately model the recovered clustering in these mock catalogues on scales 30 -- 200 Mpc/h. Applying this analysis to robustly measure parameters describing the growth history of the Universe from the SDSS-II data, gives $f(z=0.25)σ_8(z=0.25)=0.3512\pm0.0583$ and $f(z=0.37)σ_8(z=0.37)=0.4602\pm0.0378$ when no prior is imposed on the growth-rate, and the background geometry is assumed to follow a $Λ$CDM model with the WMAP + SNIa priors. The standard WMAP constrained $Λ$CDM model with General Relativity predicts $f(z=0.25)σ_8(z=0.25)=0.4260\pm0.0141$ and $f(z=0.37)σ_8(z=0.37)=0.4367\pm0.0136$, which is fully consistent with these measurements.

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arXiv2011

Cosmological Measurements with Forthcoming Radio Continuum Surveys

We present forecasts for constraints on cosmological models which can be obtained by forthcoming radio continuum surveys: the wide surveys with the LOw Frequency ARray (LOFAR), Australian Square Kilometre Array Pathfinder (ASKAP) and the Westerbork Observations of the Deep APERTIF Northern sky (WODAN). We use simulated catalogues appropriate to the planned surveys to predict measurements obtained with the source auto-correlation, the cross-correlation between radio sources and CMB maps (the Integrated Sachs-Wolfe effect), the cross-correlation of radio sources with foreground objects due to cosmic magnification, and a joint analysis together with the CMB power spectrum and supernovae. We show that near future radio surveys will bring complementary measurements to other experiments, probing different cosmological volumes, and having different systematics. Our results show that the unprecedented sky coverage of these surveys combined should provide the most significant measurement yet of the Integrated Sachs-Wolfe effect. In addition, we show that using the ISW effect will significantly tighten constraints on modified gravity parameters, while the best measurements of dark energy models will come from galaxy auto-correlation function analyses. Using the combination of EMU and WODAN to provide a full sky survey, it will be possible to measure the dark energy parameters with an uncertainty of \{$σ(w_0) = 0.05$, $σ(w_a) = 0.12$\} and the modified gravity parameters \{$σ(η_0) = 0.10$, $σ(μ_0) = 0.05$\}, assuming Planck CMB+SN(current data) priors. Finally, we show that radio surveys would detect a primordial non-Gaussianity of $f_{\rm NL}$ = 8 at 1-$σ$ and we briefly discuss other promising probes.

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arXiv2011

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.

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arXiv2011

Disentangling star formation and merger growth in the evolution of Luminous Red Galaxies

We introduce a novel technique for empirically understanding galaxy evolution. We use empirically determined stellar evolution models to predict the past evolution of the Sloan Digital Sky Survey (SDSS-II) Luminous Red Galaxy (LRG) sample without any a-priori assumption about galaxy evolution. By carefully contrasting the evolution of the predicted and observed number and luminosity densities we test the passive evolution scenario for galaxies of different luminosity, and determine minimum merger rates. We find that the LRG population is not purely coeval, with some of galaxies targeted at z<0.23 and at z>0.34 showing different dynamical growth than galaxies targeted throughout the sample. Our results show that the LRG population is dynamically growing, and that this growth must be dominated by the faint end. For the most luminous galaxies, we find lower minimum merger rates than required by previous studies that assume passive stellar evolution, suggesting that some of the dynamical evolution measured previously was actually due to galaxies with non-passive stellar evolution being incorrectly modelled. Our methodology can be used to identify and match coeval populations of galaxies across cosmic times, over one or more surveys.

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arXiv2011

Galaxy Clustering in the Completed SDSS Redshift Survey: The Dependence on Color and Luminosity

We measure the luminosity and color dependence of galaxy clustering in the SDSS DR7 main galaxy sample, focusing on the projected correlation function w_p(r_p) of volume-limited samples. We interpret our measurements using halo occupation distribution (HOD) modeling assuming a Lambda-CDM cosmology. The amplitude of w_p(r_p) grows slowly with luminosity for L < L_* and increases sharply at higher luminosities, with bias factor b(>L)=1.06+0.23(L/L_*)^{1.12}. At fixed luminosity, redder galaxies have a stronger and steeper w_p(r_p), a trend that runs steadily from the bluest galaxies to the reddest galaxies. The individual luminosity trends for the red and blue galaxy populations are strikingly different. Blue galaxies show a slow but steady increase of w_p(r_p) with luminosity, at all scales. The large-scale clustering of red galaxies shows little luminosity dependence until a sharp increase at L > 4L_*, but the lowest luminosity red galaxies (0.04-0.25 L_*) show very strong clustering on scales r_p < 2 Mpc/h. Most of the observed trends can be naturally understood within the LCDM+HOD framework. The growth of w_p(r_p) with luminosity reflects an overall shift in the halo mass scale, in particular an increase in the minimum host halo mass Mmin. The mass at which a halo has, on average, one satellite galaxy brighter than L is M_1 ~ 17 Mmin(L) over most of the luminosity range. The growth and steepening of w_p(r_p) for redder galaxies reflects the increasing fraction of galaxies that are satellite systems in high mass halos instead of central systems in low mass halos, a trend that is especially marked at low luminosities. Our extensive measurements, provided in tabular form, will allow detailed tests of theoretical models of galaxy formation, a firm grounding of semi-empirical models of the galaxy population, and new cosmological tests.

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arXiv2011

Understanding the faint red galaxy population using large-scale clustering measurements from SDSS DR7

We use data from the SDSS to investigate the evolution of the large-scale galaxy bias as a function of luminosity for red galaxies. We carefully consider correlation functions of galaxies selected from both photometric and spectroscopic data, and cross-correlations between them, to obtain multiple measurements of the large-scale bias. We find, for our most robust analyses, a strong increase in bias with luminosity for the most luminous galaxies, an intermediate regime where bias does not evolve strongly over a range of two magnitudes in galaxy luminosity, and no evidence for an upturn in bias for fainter red galaxies. Previous work has found an increase in bias to low luminosities that has been widely interpreted as being caused by a strong preference for red dwarf galaxies to be satellites in the most massive halos. We can recover such an upturn in bias to faint luminosities if we push our measurements to small scales, and include galaxy clustering measurements along the line-of-sight, where we expect non-linear effects to be the strongest. The results that we expect to be most robust suggest that the low luminosity population of red galaxies is not dominated by satellite galaxies occupying the most massive haloes.

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arXiv2010

The stellar evolution of Luminous Red Galaxies, and its dependence on colour, redshift, luminosity and modelling

We present a series of colour evolution models for Luminous Red Galaxies (LRGs) in the 7th spectroscopic data release of the Sloan Digital Sky Survey (SDSS), computed using the full-spectrum fitting code VESPA on high signal-to-noise stacked spectra. The colour-evolution models are computed as a function of colour, luminosity and redshift, and we do not a-priori assume that LRGs constitute a uniform population of galaxies in terms of stellar evolution. By computing star-formation histories from the fossil record, the measured stellar evolution of the galaxies is decoupled from the survey's selection function, which also evolves with redshift. We present these evolutionary models computed using three different sets of Stellar Population Synthesis (SPS) codes. We show that the traditional fiducial model of purely passive stellar evolution of LRGs is broadly correct, but it is not sufficient to explain the full spectral signature. We also find that higher-order corrections to this model are dependent on the SPS used, particularly when calculating the amount of recent star formation. The amount of young stars can be non-negligible in some cases, and has important implications for the interpretation of the number density of LRGs within the selection box as a function of redshift. Dust extinction, however, is more robust to the SPS modelling: extinction increases with decreasing luminosity, increasing redshift, and increasing r-i colour. We are making the colour evolution tracks publicly available at http://www.icg.port.ac.uk/~tojeiror/lrg_evolution/.

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arXiv2010

Neutrino masses from clustering of red and blue galaxies: a test of astrophysical uncertainties

Combining measurements of the galaxy power spectrum and the cosmic microwave background (CMB) is a powerful means of constraining the summed mass of neutrino species sum(m_nu), but is subject to systematic uncertainties due to non-linear structure formation, redshift-space distortions and galaxy bias. We empirically test the robustness of neutrino mass results to these effects by separately analyzing power spectra of red and blue galaxies from the Sloan Digital Sky Survey (SDSS-II) Data Release 7 (DR7), combined with the CMB five-year Wilkinson Microwave Anisotropy Probe (WMAP5) data. We consider fitting for a range of maximum wavenumber k using twelve different galaxy bias models. For example, using a new model based on perturbation theory and including redshift space distortions (Saito et al. 2009), the all-galaxy power spectrum combined with WMAP5 for a wavenumber range of k<0.2 Mpc/h yields 95% CL sum(m_nu)<0.46 eV. The red and blue galaxy power spectra give 0.41 and 0.63 eV respectively for this model. Using mock catalogues, we find the expected difference in these limits assuming a true neutrino mass of zero is 0.10 + or - 0.14 eV. Thus the difference of 0.22 eV between upper limits on neutrino mass for red and blue galaxies is approximately 1 sigma from the expected value. We find similar results for the other models and k ranges tested. This indicates good agreement for current data but hints at possible issues for next-generation surveys. Being able to perform such systematic tests is advantageous, and future surveys would benefit by including broad galaxy populations and luminosities that enable such a decomposition.

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arXiv2010

Simulating Redshift-Space Distortions for Galaxy Pairs with Wide Angular Separation

The analysis of Redshift-Space Distortions (RSD) within galaxy surveys provides constraints on the amplitude of peculiar velocities induced by structure growth, thereby allowing tests of General Relativity on extremely large scales. The next generation of galaxy redshift surveys, such as the Baryon Oscillation Spectroscopic Survey (BOSS), and the Euclid experiment will survey galaxies out to z=2, over 10,000--20,000 sq deg. In such surveys, galaxy pairs with large comoving separation will preferentially have a wide angular separation. In standard plane-parallel theory the displacements of galaxy positions due to RSD are assumed to be parallel for all galaxies, but this assumption will break down for wide-angle pairs. Szapudi 2004 and Papai & Szapudi 2008 provided a methodology, based on tripolar spherical harmonics expansion, for computing the redshift-space correlation function for all angular galaxy pair separations. In this paper we introduce a new procedure for analysing wide-angle effects in numerical simulations. We are able to separate, demonstrate, and fit each of the effects described by the wide-angle RSD theory. Our analysis highlights some of the nuances of dealing with wide-angle pairs, and shows that the effects are not negligible even for relatively small angles. This analysis will help to ensure the full exploitation of future surveys for RSD measurements, which are currently confined to pair separations less than \sim80 Mpc/h out to z\simeq 0.5.

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arXiv2010

The effect of redshift-space distortions on projected 2-pt clustering measurements

Although redshift-space distortions only affect inferred distances and not angles, they still distort the projected angular clustering of galaxy samples selected using redshift dependent quantities. From an Eulerian view-point, this effect is caused by the apparent movement of galaxies into or out of the sample. From a Lagrangian view-point, we find that projecting the redshift-space overdensity field over a finite radial distance does not remove all the anisotropic distortions. We investigate this effect, showing that it strongly boosts the amplitude of clustering for narrow samples and can also reduce the significance of baryonic features in the correlation function. We argue that the effect can be mitigated by binning in apparent galaxy pair-centre rather than galaxy position, and applying an upper limit to the radial galaxy separation. We demonstrate this approach, contrasting against standard top-hat binning in galaxy distance, using sub-samples taken from the Hubble Volume simulations. Using a simple model for the radial distribution expected for galaxies from a survey such as the Dark Energy Survey (DES), we show that this binning scheme will simplify analyses that will measure baryon acoustic oscillations within such galaxy samples. Comparing results from different binning schemes has the potential to provide measurements of the amplitude of the redshift-space distortions. Our analysis is relevant for other photometric redshift surveys, including those made by the Panoramic Survey Telescope & Rapid Response System (Pan-Starrs) and the Large Synoptic Survey Telescope (LSST).

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arXiv2010

Evolution of the Clustering of Photometrically Selected SDSS Galaxies

We measure the angular auto-correlation functions (w) of SDSS galaxies selected to have photometric redshifts 0.1 < z < 0.4 and absolute r-band magnitudes Mr < -21.2. We split these galaxies into five overlapping redshift shells of width 0.1 and measure w in each subsample in order to investigate the evolution of SDSS galaxies. We find that the bias increases substantially with redshift - much more so than one would expect for a passively evolving sample. We use halo-model analysis to determine the best-fit halo-occupation-distribution (HOD) for each subsample, and the best-fit models allow us to interpret the change in bias physically. In order to properly interpret our best-fit HODs, we convert each halo mass to its z = 0 passively evolved bias (bo), enabling a direct comparison of the best-fit HODs at different redshifts. We find that the minimum halo bo required to host a galaxy decreases as the redshift decreases, suggesting that galaxies with Mr < -21.2 are forming in halos at the low-mass end of the HODs over our redshift range. We use the best-fit HODs to determine the change in occupation number divided by the change in mass of halos with constant bo and we find a sharp peak at bo ~ 0.9 - corresponding to an average halo mass of ~ 10^12Msol/h. We thus present the following scenario: the bias of galaxies with Mr < -21.2 decreases as the Universe evolves because these galaxies form in halos of mass ~ 10^12Msol/h (independent of redshift), and the bias of these halos naturally decreases as the Universe evolves.

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arXiv2010

The evolution of Luminous Red Galaxies in the Sloan Digital Sky Survey 7th data release

We present a comprehensive study of the evolution of Luminous Red Galaxies (LRGs) in the latest and final spectroscopic data release of the Sloan Digital Sky Survey. We test the scenario of passive evolution of LRGs in 0.15<z<0.5, by looking at the evolution of the number and luminosity density of LRGs, as well as of their clustering. A new weighting scheme is introduced that allows us to keep a large number of galaxies in our sample and put stringent constraints on the growth and merging allowed by the data as a function of galaxy luminosity. Introducing additional luminosity-dependent weighting for our clustering analysis allows us to additionally constrain the nature of the mergers. We find that, in the redshift range probed, the population of LRGs grows in luminosity by 1.5-6 % Gyr^-1 depending on their luminosity. This growth is predominantly happening in objects that reside in the lowest-mass haloes probed by this study, and cannot be explained by satellite accretion into massive LRGs, nor by LRG-LRG merging. We find that the evolution of the brightest objects (with a K+e-corrected M_r,0.1 < -22.8) is consistent with that expected from passive evolution.

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arXiv2009

Baryon Acoustic Oscillations in the Sloan Digital Sky Survey Data Release 7 Galaxy Sample

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 (LRG) and Main samples, and also include the 2-degree Field Galaxy Redshift Survey (2dFGRS) data. Baryon Acoustic Oscillations 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 r_s(z_d)/D_V(0.275)=0.1390+/-0.0037 (2.7% accuracy), where r_s(z_d) is the comoving sound horizon at the baryon drag epoch, D_V(z)=[(1+z)^2D_A^2cz/H(z)]^(1/3), D_A(z) is the angular diameter distance and H(z) is the Hubble parameter. We find an almost independent constraint on the ratio of distances D_V(0.35)/D_V(0.2)=1.736+/-0.065, which is consistent at the 1.1sigma level with the best fit Lambda-CDM model obtained when combining our z=0.275 distance constraint with the WMAP 5-year 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 Omega_bh^2 and Omega_ch^2, and combining our BAO distance measurements with those from the Union Supernova sample, places a tight constraint on Omega_m=0.286+/-0.018 and H_0 = 68.2+/-2.2km/s/Mpc that is robust to allowing curvature and non-Lambda dark energy. This result is independent of the behaviour of dark energy at redshifts greater than those probed by the BAO and supernova measurements. (abridged)

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arXiv2009

Reconstructing the history of structure formation using redshift distortions

Measuring the statistics of galaxy peculiar velocities using redshift-space distortions is an excellent way of probing the history of structure formation. Because galaxies are expected to act as test particles within the flow of matter, this method avoids uncertainties due to an unknown galaxy density bias. We show that the parameter combination measured by redshift-space distortions, $fσ_8^{\rm mass}$ provides a good test of dark energy models, even without the knowledge of bias or $σ_8^{\rm mass}$ required to extract $f$ from this measurement (here $f$ is the logarithmic derivative of the linear growth rate, and $σ_8^{\rm mass}$ is the root-mean-square mass fluctuation in spheres with radius $8h^{-1}$Mpc). We argue that redshift-space distortion measurements will help to determine the physics behind the cosmic acceleration, testing whether it is related to dark energy or modified gravity, and will provide an opportunity to test possible dark energy clumping or coupling between dark energy and dark matter. If we can measure galaxy bias in addition, simultaneous measurement of both the overdensity and velocity fields can be used to test the validity of equivalence principle, through the continuity equation.

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arXiv2009

Cosmological Constraints from the Clustering of the Sloan Digital Sky Survey DR7 Luminous Red Galaxies

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, 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, as was adopted in the SDSS team analysis of the DR4 LRG sample (Tegmark et al. 2006). The observed halo power spectrum for 0.02 < k < 0.2 h/Mpc is well-fit by our model: chi^2 = 39.6 for 40 degrees of freedom for the best fit LCDM 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 LCDM model we find Ω_m = 0.289 +/- 0.019 and H_0 = 69.4 +/- 1.6 km/s/Mpc. Allowing for massive neutrinos in LCDM, we find \sum m_ν < 0.62 eV at the 95% 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. (2008) supernova sample, we find Ω_{tot} = 1.011 +/- 0.009 and w = -0.99 +/- 0.11 for an open cosmology with constant dark energy equation of state w.

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arXiv2008

Forecasting Cosmological Constraints from Redshift Surveys

Observations of redshift-space distortions in spectroscopic galaxy surveys offer an attractive method for observing the build-up of cosmological structure, which depends both on the expansion rate of the Universe and our theory of gravity. In this paper we present a formalism for forecasting the constraints on the growth of structure which would arise in an idealized survey. This Fisher matrix based formalism can be used to study the power and aid in the design of future surveys.

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arXiv2008

Scale Dependent Galaxy Bias in the SDSS as a function of Luminosity and Colour

It has been known for a long time that the clustering of galaxies changes as a function of galaxy type. This galaxy bias acts as a hindrance to the extraction of cosmological information from the galaxy power spectrum or correlation function. Theoretical arguments show that a change in the amplitude of the clustering between galaxies and mass on large-scales is unavoidable, but cosmological information can be easily extracted from the shape of the power spectrum or correlation function if this bias is independent of scale. Scale-dependent bias is generally small on large scales, k<0.1 h.Mpc^{-1}, but on smaller scales can affect the recovery of Ω_m.h from the measured shape of the clustering signal, and have a small effect on the Baryon Acoustic Oscillations. In this paper we investigate the transition from scale-independent to scale-dependent galaxy bias as a function of galaxy population. We use the Sloan Digital Sky Survey DR5 sample to fit various models, which attempt to parametrise the turn-off from scale-independent behaviour. For blue galaxies, we find that the strength of the turn-off is strongly dependent on galaxy luminosity, with stronger scale-dependent bias on larger scales for more luminous galaxies. For red galaxies, the scale-dependence is a weaker function of luminosity. Such trends need to be modelled in order to optimally extract the information available in future surveys, and can help with the design of such surveys.

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