Baryon acoustic oscillations (BAOs) are used to obtain precision measurements of cosmological parameters from large-scale surveys. While robust against most systematics, there are certain theoretical uncertainties that can affect BAO and galaxy clustering measurements. In this thesis I use data from the Sloan Digital Sky Survey (SDSS) to measure cosmological parameters and use N-body and smoothed-particle hydrodynamic (SPH) simulations to measure the effect of theoretical uncertainties by using halo occupation distributions (HODs). I investigate the effect of galaxy bias on BAO measurements by creating mock galaxy catalogs from large N -body simulations at z = 1. I find that there is no additional shift in the acoustic scale (0.10% ± 0.10%) for the less biased HODs (b < 3) and a mild shift (0.79% ± 0.31%) for the highly biased HODs (b > 3). I present the methodology and implementation of the simple one-step reconstruction technique introduced by Eisenstein et al. (2007) to biased tracers in N-body simulation. Reconstruction reduces the errorbars on the acoustic scale measurement by a factor of 1.5 - 2, and removes any additional shift due to galaxy bias for all HODs (0.07% ± 0.15%). Padmanabhan et al. (2012) and Xu et al. (2012) use this reconstruction technique in the SDSS DR7 data to measure Dᵥ(z = 0.35)(rᶠⁱᵈs/rs) = 1356 ± 25 Mpc. Here I use this measurement in combination with measurements from the cosmic microwave background and the supernovae legacy survey to measure various cosmological parameters. I find the data consistent with the ΛCDM Universe with a flat geometry. In particular, I measure H₀ = 69.8 ± 1.2 km/s/Mpc, w = 0.97 ± 0.17, Ωk = -0.004 ± 0.005 in the ΛCDM, wCDM, and oCDM models respectively. Next, I measure the effect of large-scale (5 Mpc) halo environment density on the HOD by using an SPH simulation at z = 0, 0.35, 0.5, 0.75, 1.0. I do not find any significant dependence of the HOD on the halo environment density for different galaxy mass thresholds, red and blue galaxies, and at different redshifts. I use the MultiDark N-body simualtion to measure the possible effect of environment density on the galaxy correlation function ℰ(r). I find that environment density enhances ℰ(r) by ∽ 3% at scales of 1 – 20h⁻¹Mpc at z = 0 and up to ∽ 12% at 0.3h⁻¹Mpc and ∽ 8% at 1 - 4h⁻¹Mpc for z = 1.

Master of Science / Department of Physics / Lado Samushia / Part 1: The redshift-space bispectrum (three point statistics) of galaxies can be used to measure key cosmological parameters. In a homogeneous Universe, the bispectrum is a function of five variables and unlike its two point statistics counterpart -- the power spectrum, which is a function of only two variables -- is difficult to analyse unless the information is somehow reduced. The most commonly considered reduction schemes rely on computing angular integrals over possible orientations of the bispectrum triangle thus reducing it to sets of functions of only three variables describing the triangle shape. We use Fisher information formalism to study the information loss associated with this angular integration. We find that most of the information is in the azimuthal averages of the first three even multipoles. This suggests that the bispectrum of every configuration can be reduced to just three numbers (instead of a 2D function) without significant loss of cosmologically relevant information. Part 2: One way of enhancing the cosmological information extracted from the clustering of galaxies is by weighting the galaxy field. The most widely used weighting schemes assign weights to galaxies based on the average local density in the region and their bias with respect to the dark matter field. They are designed to minimize the fractional variance of the galaxy power-spectrum. We demonstrate that the currently used bias dependent weighting scheme can be further optimized for specific cosmological parameters. Part 3: Choice of the box-size of a cosmological simulation involves a crucial trade-off between accuracy and complexity. We use Lagrangian perturbation theory to study the effects of box size on the predicted power spectrum and Baryon Acoustic Oscillation ruler. We find that although the optimal size depends on the final redshift of evolution, in general, the 2-point statistics of relevant scales is fairly accurate for a simulation box-size of length greater than 1000 Mpc.

In this era of high-precision cosmology we are able to measure and predict properties of the large-scale structure of our Universe to a fine degree. However we still lack a clear and tested understanding of the effects of the large-scale environments on galaxies and their host halos. This thesis focuses on bettering our understanding of this issue by investigating the dependence of galaxies and halos on their location within the cosmic web. An algorithm based on the tidal tensor prescription is developed and applied to the MDR1 1 (h-1Gpc)3 dark matter simulation to classify the geometric environment of every location in the simulated volume as one of the four components of the cosmic web; voids, sheets, filaments and knots. Conditional halo mass functions are extracted to investigate the influence of tidal forces on the abundances and mass distribution of dark matter halos. A theoretical framework based on Gaussian statistics is presented and used to derive predictions for halo abundances in different geometric environments. The Gaussian theory predicts no coupling of tidal forces and, hence, that the halo mass function is independent of geometric environment for a given local mass density. It is shown that the halo mass functions extracted from the simulation are fully consistent with this picture. It is then shown how this method of classifying geometric environments can be extended to observational datasets. The Galaxy And Mass Assembly (GAMA) spectroscopic redshift survey, with its wide field and high completeness, is excellently suited to this study. The geometric environments of the three equatorial GAMA fields are classified, following a thorough analysis of the additional uncertainties introduced when moving to observational datasets. Additionally, the geometric environments of the GAMA galaxies and groups are classified, allowing the influence of the cosmic web on large-scale structure to be investigated. Both the galaxy luminosity function and the group mass function within the observed cosmic web are studied and no evidence of a direct impact of the web is seen. It is found that all modulations can be fully attributed to the indirect dependence of these properties on the local matter overdensity. Whilst these results indicate that there is no strong dependence of the scalar properties of large-scale structure on geometric environment, the final investigation of this thesis presents an attempt to look in more detail at the environmental dependence of stellar properties by investigating stellar-formation histories within the cosmic web.

The shapes of cluster central galaxies are not randomly oriented, but rather exhibit coherent alignments with the shapes of their parent clusters as well as with the surrounding large-scale structures. In this work, we aim to identify the galaxy and cluster quantities that most strongly predict the central galaxy alignment phenomenon among a large parameter space with a sample of 8237 clusters and 94 817 members within 0.1 < z < 0.35, based on the red-sequence Matched-filter Probabilistic Percolation cluster catalogue constructed from the Sloan Digital Sky Survey. We first quantify the alignment between the projected central galaxy shapes and the distribution of member satellites, to understand what central galaxy and cluster properties most strongly correlate with these alignments. Next, we investigate the angular segregation of satellites with respect to their central galaxy major axis directions, to identify the satellite properties that most strongly predict their angular segregation. We find that central galaxies are more aligned with their member galaxy distributions in clusters that are more elongated and have higher richness, and for central galaxies with larger physical size, higher luminosity and centring probability, and redder colour. Satellites with redder colour, higher luminosity, located closer to the central galaxy, and with smaller ellipticity show a stronger angular segregation towards their central galaxy major axes. Finally, we provide physical explanations for some of the identified correlations, and discuss the connection to theories of central galaxy alignments, the impact of primordial alignments with tidal fields, and the importance of anisotropic accretion.

Observational surveys which probe our universe deeper and deeper into the nonlinear regime of structure formation are becoming increasing accurate. This makes numerical simulations an essential tool for theory to be able to predict phenomena at comparable scales. In the first part of this thesis we study the behaviour of cosmological models involving a scalar field. We are particularly interested in the existence of fixed points of the dynamical system and the behaviour of the system in their vicinity. Upon addition of spatial curvature to the single-scalar field model with an exponential potential, canonical kinetic term, and a matter fluid, we demonstrate the existence of two extra fixed points that are not present in the case without curvature. We also analyse the evolution of the equation-of-state parameter. In the second part, we numerically simulate collisionless particles in the weak field approximation to General Relativity, with large gradients of the fields and relativistic velocities allowed. To reduce the complexity of the problem and enable high resolution simulations, we consider the spherically symmetric case. Comparing numerical solutions to the exact Schwarzschild and Lemaître-Tolman-Bondi solutions, we show that the scheme we use is more accurate than a Newtonian scheme, correctly reproducing the leading-order post-Newtonian behaviour. Furthermore, by introducing angular momentum, configurations corresponding to bound objects are found. In the final part, we simulate the conditions under which one would expect to form ultracompact minihalos, dark matter halos with a steep power-law profile. We show that an isolated object exhibits the profile predicted analytically. Embedding this halo in a perturbed environment we show that its profile becomes progressively more similar to the Navarro-Frenk-White profile with increasing amplitude of perturbations. Next, we boost the power spectrum at a very early redshift during radiation domination on a chosen scale and simulate clustering of dark matter particles at this scale until low redshift. In this scenario halos form earlier, have higher central densities, and are more compact.

In this work we explore three-point statistics applied to the large-scale structure in our Universe. Three-point statistics, such as the bispectrum, encode information not accessible via the standard analysis method-the power spectrum-and thus provide the potential for greatly improving current constraints on cosmological parameters. They also present us with additional challenges, and we focus on two of these arising from a measurement as well as modelling point of view. The first challenge we address is the covariance matrix of the bispectrum, as its precise estimate is required when performing likelihood analyses. Covariance matrices are usually estimated from a set of independent simulations, whose minimum number scales with the dimension of the covariance matrix. Because there are many more possibilities of finding triplets of galaxies than pairs, compared to the power spectrum this approach becomes rather prohibitive. With this motivation in mind, we explore a novel alternative to the bispectrum: the line correlation function (LCF). It specifically targets information in the phases of density modes that are invisible to the power spectrum, making it a potentially more efficient probe than the bispectrum, which measures a combination of amplitudes and phases. We derive the covariance properties and the impact of shot noise for the LCF and compare these theoretical predictions with measurements from N-body simulations. Based on a Fisher analysis we assess the LCF's sensitivity on cosmological parameters, finding that it is particularly suited for constraining galaxy bias parameters and the amplitude of fluctuations. As a next step we contrast the Fisher information of the LCF with the full bispectrum and two other recently proposed alternatives. We show that the LCF is unlikely to achieve a lossless compression of the bispectrum information, whereas a modal decomposition of the bispectrumcan reduce the size of the covariancematrix by at least an order of magnitude. The second challenge we consider in this work concerns the relation between the dark matter field and luminous tracers, such as galaxies. Accurate knowledge of this galaxy bias relation is required in order to reliably interpret the data gathered by galaxy surveys. On the largest scales the dark matter and galaxy densities are linearly related, but a variety of additional terms need to be taken into account when studying clustering on smaller scales. These have been fully included in recent power spectrumanalyses, whereas the bispectrummodel relied on simple prescriptions that were likely extended beyond their realm of validity. In addition, treating power spectrumand bispectrum on different footings means that the two models become inconsistent on small scales. We introduce a new formalism that allows us to elegantly compute the lacking bispectrum contributions from galaxy bias, without running into the renormalization problem. Furthermore, we fit our new model to simulated data by implementing these contributions into a likelihood code. We show that they are crucial in order to obtain results consistent with those fromthe power spectrum, and that the bispectrum retains its capability of significantly reducing uncertainties in measured parameters when combined with the power spectrum.

Thesis (Ph. D.)--University of Chicago, Department of Astronomy & Astrophysics, August 2002. / Includes bibliographical references. Also available on the Internet.

We study the orientations of satellite galaxies in redMaPPer clusters constructed from the Sloan Digital Sky Survey at 0.1 < z < 0.35 to determine whether there is any preferential tendency for satellites to point radially towards cluster centres. We analyse the satellite alignment (SA) signal based on three shape measurement methods (re-Gaussianization, de Vaucouleurs, and isophotal shapes), which trace galaxy light profiles at different radii. The measured SA signal depends on these shape measurement methods. We detect the strongest SA signal in isophotal shapes, followed by de Vaucouleurs shapes. While no net SA signal is detected using re-Gaussianization shapes across the entire sample, the observed SA signal reaches a statistically significant level when limiting to a subsample of higher luminosity satellites. We further investigate the impact of noise, systematics, and real physical isophotal twisting effects in the comparison between the SA signal detected via different shape measurement methods. Unlike previous studies, which only consider the dependence of SA on a few parameters, here we explore a total of 17 galaxy and cluster properties, using a statistical model averaging technique to naturally account for parameter correlations and identify significant SA predictors. We find that the measured SA signal is strongest for satellites with the following characteristics: higher luminosity, smaller distance to the cluster centre, rounder in shape, higher bulge fraction, and distributed preferentially along the major axis directions of their centrals. Finally, we provide physical explanations for the identified dependences and discuss the connection to theories of SA.

In this thesis, I investigate the spatial distribution of radio sources, and quantify their clustering strength over a range of redshifts, up to z _ 2:2, using various forms of the correlation function measured with data from several multi-wavelength surveys. I present the optical spectra of 30 radio AGN (S1:4 > 100 mJy) in the GAMA/H-ATLAS fields, for which emission line redshifts could be deduced, from observations of 79 target sources with the EFOSC2 spectrograph on the NTT. The mean redshift of these sources is z = 1:2; 12 were identified as quasars (40 per cent), and 6 redshifts (out of 24 targets) were found for AGN hosts to multiple radio components. While obtaining spectra for hosts of these multi-component sources is possible, their lower success rate highlights the difficulty in acheiving a redshift-complete radio sample. Taking an existing spectroscopic redshift survey (GAMA) and radio sources from the FIRST survey (S1:4 > 1 mJy), I then present a cross-matched radio sample with 1,635 spectroscopic redshifts with a median value of z = 0:34. The spatial correlation function of this sample is used to find the redshiftspace (s0) and real-space correlation lengths (r0 _ 8:2 h 1Mpc), and a mass bias of _1.9. Insight into the redshift-dependence of these quantities is gained by using the angular correlation function and Limber inversion to measure the same spatial clustering parameters. Photometric redshifts from SDSS/UKIDSS are incorporated to produce a larger matched radio sample at z ' 0:48 (and low- and high-redshift subsamples at z ' 0:30 and z ' 0:65), while their redshift distribution is subtracted from that taken from the SKADS radio simulations to estimate the redshift distribution of the remaining unmatched sources (z ' 1:55). The observed bias evolution over this redshift range is compared with model predictions based on the SKADS simulations, with good agreement at low redshift. The bias found at high redshift significantly exceeds these predictions, however, suggesting a more massive population of galaxies than expected, either due to the relative proportions of different radio sources, or a greater typical halo mass for the high-redshift sources. Finally, the reliance on a model redshift distribution to reach to higher redshifts is removed, as the angular cross-correlation function is used with deep VLA data (S1:4 > 90 _Jy) and optical/IR data from VIDEO/CFHTLS (Ks < 23:5) over 1 square degree. With high-quality photometric redshifts up to z _ 4, and a high signal-to-noise clustering measurement (due to the _100,000 Ks-selected galaxies), I am able to find the bias of a matched sample of only 766 radio sources (as well as of v vi the VIDEO sources), divided into 4 redshift bins reaching a median bias at z ' 2:15. Again, at high redshift, the measured bias appears to exceed the prediction made from the SKADS simulations. Applying luminosity cuts to the radio sample at L > 1023 WHz 1 and higher (removing any non-AGN sources), I find a bias of 8–10 at z _ 1:5, considerably higher than for the full sample, and consistent with the more numerous FRI AGN having similar mass to the FRIIs (M _ 1014 M_), contrary to the assumptions made in the SKADS simulations. Applying this adjustment to the model bias produces a better fit to the observations for the FIRST radio sources cross-matched with GAMA/SDSS/UKIDSS, as well as for the high-redshift radio sources in VIDEO. Therefore, I have shown that we require a more robust model of the evolution of AGN, and their relation to the underlying dark matter distribution. In particular, understanding these quantities for the abundant FRI population is crucial if we are to use such sources to probe the cosmological model as has been suggested by a number of authors (e.g. Raccanelli et al., 2012; Camera et al., 2012; Ferramacho et al., 2014).

We present techniques for obtaining precision distance measurements using the baryon acoustic oscillations (BAO) through controlling systematics and reducing statistical uncertainties. Using the resulting distance-redshift relation, we can infer cosmological parameters such as w, the equation of state of dark energy. We introduce a new statistic, ɷ(l)(r(s)), for BAO analysis that affords better control over systematics. It is computed by band-filtering the power spectrum P(k) or the correlation function ξ(r) to extract the BAO signal. This is conducive to several favourable outcomes. We compute ɷ(l)(r(s)) from 44 simulations and compare the results to P(k) and ξ(r). We find that the acoustic scales and theoretical errors we measure are consistent between all three statistics. We demonstrate the first application of reconstruction to a galaxy redshift survey. Reconstruction is designed to partially undo the effects of non-linear structure growth on the BAO, allowing more precise measurements of the acoustic scale. We also present a new method for deriving a smooth covariance matrix based on a Gaussian model. In addition, we develop and perform detailed robustness tests on the ξ(r) model we employ to extract the BAO scale from the data. Using these methods, we obtain spherically-averaged distances to z = 0.35 and z = 0.57 from SDSS DR7 and DR9 with 1.9% and 1.7% precision respectively. Combined with WMAP7 CMB observations, SNLS3 data and BAO measurements from 6dF, we measure w = -1.08 ± 0.08 assuming a wCDM cosmology. This represents a ~8% measurement of w and is consistent with a cosmological constant.The preceding does not capture the expansion history of the universe, H(z), encoded in the line-of-sight distance scale. To disentangle H(z), we exploit the anisotropic BAO signal that arises if we assume the wrong cosmology when calculating the clustering distribution. Since we expect the BAO signal to be isotropic, we can use the magnitude of the anisotropy to separately measure H(z) and D(A)(z). We apply our simple models to SDSS DR7 data and obtain a ~3.6% measurement of D(A)(z=0.35) and a ~8.4% measurement of H(z = 0.35).