Anisotropic measurements of the Baryon Acoustic Oscillation (BAO) feature within a galaxy survey enable joint inference about the Hubble parameter $H(z)$ and angular diameter distance $D_A(z)$. These measurements are typically obtained from moments o
f the measured 2-point clustering statistics, with respect to the cosine of the angle to the line of sight $mu$. The position of the BAO features in each moment depends on a combination of $D_A(z)$ and $H(z)$, and measuring the positions in two or more moments breaks this parameter degeneracy. We derive analytic formulae for the parameter combinations measured from moments given by Legendre polynomials, power laws and top-hat Wedges in $mu$, showing explicitly what is being measured by each in real-space for both the correlation function and power spectrum, and in redshift-space for the power spectrum. The large volume covered by modern galaxy samples means that the correlation function can be well approximated as having no correlations at different $mu$ on the BAO scale, and that the errors on this scale are approximately independent of $mu$. Using these approximations, we derive the information content of various moments. We show that measurements made using either the monopole and quadrupole, or the monopole and $mu^2$ power-law moment, are optimal for anisotropic BAO measurements, in that they contain all of the available information using two moments, the minimal number required to measure both $H(z)$ and $D_A(z)$. We test our predictions using 600 mock galaxy samples, matched to the SDSS-III Baryon Oscillation Spectroscopic Survey CMASS sample, finding a good match to our analytic predictions. Our results should enable the optimal extraction of information from future galaxy surveys such as eBOSS, DESI and Euclid.
We present a detailed derivation of the observed galaxy number over-density on cosmological scales up to second order in perturbation theory. We include all relativistic effects that arise from observing on the past lightcone. The derivation is in a
general gauge, and applies to all dark energy models (including interacting dark energy) and many modified gravity models. The result will be important for accurate cosmological parameter estimation, including non-Gaussianity, since all projection effects need to be taken into account. It also offers the potential for new probes of General Relativity, dark energy and modified gravity. This paper accompanies Paper I which presents the key results for the concordance model in Poisson gauge.
We present the galaxy number overdensity up to second order in redshift space on cosmological scales for a concordance model. The result contains all general relativistic effects up to second order that arise from observing on the past light cone, in
cluding all redshift effects, lensing distortions from convergence and shear, and contributions from velocities, Sachs-Wolfe, integrated SW and time-delay terms. This result will be important for accurate calculation of the bias on estimates of non-Gaussianity and on precision parameter estimates, introduced by nonlinear projection effects.
We investigate the dependence of the Vainshtein screening mechanism on the cosmic web morphology of both dark matter particles and halos as determined by ORIGAMI. Unlike chameleon and symmetron screening, which come into effect in regions of high den
sity, Vainshtein screening instead depends on the dimensionality of the system, and screened bodies can still feel external fields. ORIGAMI is well-suited to this problem because it defines morphologies according to the dimensionality of the collapsing structure and does not depend on a smoothing scale or density threshold parameter. We find that halo particles are screened while filament, wall, and void particles are unscreened, and this is independent of the particle density. However, after separating halos according to their large scale morphological environment, we find no difference in the screening properties of halos in filaments versus halos in clusters. We find that the fifth force enhancement of dark matter particles in halos is greatest well outside the virial radius. We confirm the theoretical expectation that even if the internal field is suppressed by the Vainshtein mechanism, the object still feels the fifth force generated by the external fields, by measuring peculiar velocities and velocity dispersions of halos. Finally, we investigate the morphology and gravity model dependence of halo spins, concentrations, and shapes.
Doppler lensing is the apparent change in object size and magnitude due to peculiar velocities. Objects falling into an overdensity appear larger on its near side, and smaller on its far side, than typical objects at the same redshifts. This effect d
ominates over the usual gravitational lensing magnification at low redshift. Doppler lensing is a promising new probe of cosmology, and we explore in detail how to utilize the effect with forthcoming surveys. We present cosmological simulations of the Doppler and gravitational lensing effects based on the Millennium simulation. We show that Doppler lensing can be detected around stacked voids or unvirialised over-densities. New power spectra and correlation functions are proposed which are designed to be sensitive to Doppler lensing. We consider the impact of gravitational lensing and intrinsic size correlations on these quantities. We compute the correlation functions and forecast the errors for realistic forthcoming surveys, providing predictions for constraints on cosmological parameters. Finally, we demonstrate how we can make 3-D potential maps of large volumes of the Universe using Doppler lensing.
We measure the redshift evolution of the bar fraction in a sample of 2380 visually selected disc galaxies found in Cosmic Evolution Survey (COSMOS) Hubble Space Telescope (HST) images. The visual classifications used to identify both the disc sample
and to indicate the presence of stellar bars were provided by citizen scientists via the Galaxy Zoo: Hubble (GZH) project. We find that the overall bar fraction decreases by a factor of two, from 22+/-5% at z=0.4 (tlb = 4.2 Gyr) to 11+/-2% at z=1.0 (tlb = 7.8 Gyr), consistent with previous analysis. We show that this decrease, of the strong bar fraction in a volume limited sample of massive disc galaxies [stellar mass limit of log(Mstar/Msun) > 10.0], cannot be due to redshift dependent biases hiding either bars or disc galaxies at higher redshifts. Splitting our sample into three bins of mass we find that the decrease in bar fraction is most prominent in the highest mass bin, while the lower mass discs in our sample show a more modest evolution. We also include a sample of 98 red disc galaxies. These galaxies have a high bar fraction (45+/-5%), and are missing from other COSMOS samples which used SED fitting or colours to identify high redshift discs. Our results are consistent with a picture in which the evolution of massive disc galaxies begins to be affected by slow (secular) internal process at z~1. We discuss possible connections of the decrease in bar fraction to the redshift, including the growth of stable disc galaxies, mass evolution of the gas content in disc galaxies, as well as the mass dependent effects of tidal interactions.
We present the distance measurement to z = 0.32 using the 11th data release of the Sloan Digital Sky Survey-III Baryon Acoustic Oscillation Survey (BOSS). We use 313,780 galaxies of the low-redshift (LOWZ) sample over 7,341 square-degrees to compute
$D_V = (1264 pm 25)(r_d/r_{d,fid})$ - a sub 2% measurement - using the baryon acoustic feature measured in the galaxy two-point correlation function and power-spectrum. We compare our results to those obtained in DR10. We study observational systematics in the LOWZ sample and quantify potential effects due to photometric offsets between the northern and southern Galactic caps. We find the sample to be robust to all systematic effects found to impact on the targeting of higher-redshift BOSS galaxies, and that the observed north-south tensions can be explained by either limitations in photometric calibration or by sample variance, and have no impact on our final result. Our measurement, combined with the baryonic acoustic scale at z = 0.57, is used in Anderson et al. (2013a) to constrain cosmological parameters.
We apply a new method to measure primordial non-Gaussianity, using the cross-correlation between galaxy surveys and the CMB lensing signal to measure galaxy bias on very large scales, where local-type primordial non-Gaussianity predicts a $k^2$ diver
gence. We use the CMB lensing map recently published by the Planck collaboration, and measure its external correlations with a suite of six galaxy catalogues spanning a broad redshift range. We then consistently combine correlation functions to extend the recent analysis by Giannantonio et al. (2013), where the density-density and the density-CMB temperature correlations were used. Due to the intrinsic noise of the Planck lensing map, which affects the largest scales most severely, we find that the constraints on the galaxy bias are similar to the constraints from density-CMB temperature correlations. Including lensing constraints only improves the previous statistical measurement errors marginally, and we obtain $ f_{mathrm{NL}} = 12 pm 21 $ (1$sigma$) from the combined data set. However, the lensing measurements serve as an excellent test of systematic errors: we now have three methods to measure the large-scale, scale-dependent bias from a galaxy survey: auto-correlation, and cross-correlation with both CMB temperature and lensing. As the publicly available Planck lensing maps have had their largest-scale modes at multipoles $l<10$ removed, which are the most sensitive to the scale-dependent bias, we consider mock CMB lensing data covering all multipoles. We find that, while the effect of $f_{mathrm{NL}}$ indeed increases significantly on the largest scales, so do the contributions of both cosmic variance and the intrinsic lensing noise, so that the improvement is small.
We study the clustering of galaxies, as a function of their colour, from Data Release Ten (DR10) of the SDSS-III Baryon Oscillation Spectroscopic Survey. We select 122,967 galaxies with 0.43 < z < 0.7 into a Blue sample and 131,969 into a Red sample
based on k+e corrected (to z=0.55) r-i colours and i band magnitudes. The samples are chosen to each contain more than 100,000 galaxies, have similar redshift distributions, and maximize the difference in clustering amplitude. The Red sample has a 40% larger bias than the Blue (b_Red/b_Blue = 1.39+-0.04), implying the Red galaxies occupy dark matter halos with an average mass that is 0.5 log Mo greater. Spherically averaged measurements of the correlation function, xi 0, and the power spectrum are used to locate the position of the baryon acoustic oscillation (BAO) feature of both samples. Using xi 0, we obtain distance scales, relative to our reference LCDM cosmology, of 1.010+-0.027 for the Red sample and 1.005+-0.031 for the Blue. After applying reconstruction, these measurements improve to 1.013+/-0.020 for the Red sample and 1.008+-0.026 for the Blue. For each sample, measurements of xi 0 and the second multipole moment, xi 2, of the anisotropic correlation function are used to determine the rate of structure growth, parameterized by fsigma 8. We find fsigma 8,Red = 0.511+-0.083, fsigma 8,Blue = 0.509+/-0.085, and fsigma 8,Cross = 0.423+-0.061 (from the cross-correlation between the Red and Blue samples). We use the covariance between the bias and growth measurements obtained from each sample and their cross-correlation to produce an optimally-combined measurement of fsigma 8,comb = 0.443+-0.055. In no instance do we detect significant differences in distance scale or structure growth measurements obtained from the Blue and Red samples.
