The object of this thesis is to present various applications of the theory of cosmological perturbations. Within are contained a number of manuscripts, each concerned with a separate aspect of the theory. The thesis itself begins with a general overview of cosmological perturbation theory designed to be accessible to the non-specialist. Both the classical and quantum first order theory are considered. Back-reaction, via the formalism of the Effective Energy Momentum Tensor (EEMT) is reviewed. Subsequent chapters are more specialized dealing with various applications of the theory. At first order, topics discussed include the classicalization of cosmological perturbations (chapter 2), and the effects of including the dilaton and its fluctuations on a novel mechanism for the production of inhomogeneities in string gas cosmology (chapter 3). At second order, an original solution to the Dark Energy problem is proposed (chapter 4), and the effects of back-reaction on the power spectrum, including the spectral index and the gaussianity, are examined (chapter 5).

Weak gravitational lensing is a powerful astronomical tool for constraining cosmological parameters that is entering its prime. Lensing occurs because gravitational fields deflect light rays and measuring this deflection through a statistic known as cosmic shear allows us to directly measure the properties of dark matter and dark energy on large scales. In principle, gravitational lensing is a clean probe of the cosmology of the Universe, as it depends on gravity alone and not on incomplete astrophysical models or approximations. In practice, however, there are several factors that limit the accuracy and precision of lensing measurements. These include accurate measurement of galaxy shapes, correctly accounting for distortions to galaxy images due to the point spread function of the telescope, the presence of intrinsic alignments (IAs) of galaxy shapes due to physical processes, and inaccuracies in commonly-used galaxy photometric redshift information. These effects may all introduce systematic errors in lensing measurements which must be carefully accounted for to ensure that cosmological constraints from lensing are unbiased and as precise as possible. The Canada-France-Hawaii-Telescope Lensing Survey (CFHTLenS) is the largest weak lensing survey completed to date, covering 154 square degrees of the sky in 5 optical bands, with photometric redshift information for every survey galaxy. With lensing measurements from more galaxies than ever before, the statistical uncertainties on parameter estimates will be the lowest ever achieved from weak lensing. If left unaccounted for, sources of systematic error would dominate over the statistical uncertainty, potentially biasing parameter estimates catastrophically. A technique known as tomography in which galaxies are sorted into bins based on their redshift can help constrain cosmological parameters more precisely. This is because utilising the redshifts of survey galaxies retains cosmological information that would otherwise be lost, such as the behaviour of dark energy and the growth of structure over time. Tomography, however, increases the demand for systematics-free galaxy catalogues as the technique is strongly sensitive to the IA signal and photometric redshift errors. Therefore, future lensing analyses will require a more sophisticated treatment of these effects to extract maximal information from the lensing signal. A thorough understanding of the error on lensing measurements is necessary in order to produce meaningful cosmological constraints. One of the key features of cosmic shear is that it is highly correlated over di erent angular scales, meaning that error estimates must take into account the covariance of the data over different angular scales, and in the case of tomography, between different redshift bins. The behaviour and size of the (inverse) covariance matrix is one of the limiting factors in such a cosmological likelihood analysis, so constructing an accurate, unbiased estimate of the covariance matrix inverse is essential to cosmic shear analysis. This thesis presents work to optimise tomographic weak lensing analysis and achieve the tightest parameter constraints possible for a CFHTLenS-like survey. N-body simulations and Gaussian shear fields incorporating an IA model (known as the `non-linear alignment' model) with a free parameter are used to estimate fully tomographic covariance matrices of cosmic shear for CFHTLenS. We simultaneously incorporate for the first time the error contribution expected from the non-linear alignment model for IAs and realistic photometric redshift uncertainties as measured from the CFHTLenS. We find that non-Gaussian simulations that incorporate nonlinearity on small scales are needed to ensure the covariance is not underestimated, and that the covariance matrix is shot-noise dominated for almost all tomographic correlations. The number of realisations of the simulations used to estimate the covariance places a hard limit on the maximum number of tomographic bins that one can use in an analysis. Given the available number of lines of sight generated from CFHTLenS-like simulations, we find that up to ~ 15 tomographic bins may be utilised in a likelihood analysis. The estimated tomographic covariance matrices are used in a least-squares likelihood analysis in order to find the combination of both angular and tomographic bins that gives the tightest constraints on some key cosmological parameters. We find that the optimum binning is somewhat degenerate, with around 6 tomographic and 8 angular bins being optimal, and limited by the available number of realisations of the simulations used to estimate the covariance. We also investigate the bias on best- t parameter estimates that occurs if IAs or photometric redshift errors are neglected. With our choice of IA model, the effect of neglecting IAs on the best- t cosmological parameters is not significant for a CFHTLenS-like survey, although this may not be true if the IA signal differs substantially from the model, or for future wide-field surveys with much smaller statistical uncertainties. Similarly, neglecting photometric redshift errors does not result in significant bias, although we apply similar caveats. Finally, we apply the results of this optimisation to the CFHTLenS cosmic shear data, performing a preliminary analysis of the shear correlation function to produce both 2D and optimal tomographic cosmological constraints. From 6-bin tomography, we constrain the matter density parameter Ωm = 0:419+0:123-0:090, the amplitude of the matter power spectrum σ8 = 0:623+0:101 -0:084 and the amplitude parameter of the non-linear alignment model, A = -1:161+1:163 -0:597. We perform this analysis to test the validity and limitations of the optimal binning on real data and find that 6-bin tomography improves parameter constraints considerably, albeit not as much as when performed on simulated data. This analysis represents an important step in the development of techniques to optimise the recovery of lensing information and hence cosmological constraints, while simultaneously accounting for potential sources of bias in shear analysis.

The timescape cosmology represents a potentially viable alternative to the standard homogeneous and isotropic Friedmann--Lemaître--Robertson--Walker (FLRW) cosmology, without the need for dark energy. This thesis first extends the previous work on the timescape cosmology to include a radiation component in the evolution equations for the timescape cosmology and tests of the timescape model are then performed against the Cosmic Microwave Background (CMB) temperature anisotropies from the Planck satellite. Although average cosmic evolution in the timescape scenario only differs substantially from that of FLRW cosmologies at relatively late epochs when the contribution from the energy density of radiation is negligible, a full solution of the Buchert equations to incorporate radiation is necessary to smoothly match parameters to the epoch of photon decoupling and to obtain constraints from CMB data. Here we have extended the matter-dominated solution found in earlier work to include radiation, providing series solutions at early times and an efficient numerical integration strategy for generating the complete solution. To analyse the spectrum of CMB anisotropies in the timescape cosmology we exploit the fact that the timescape cosmology is extremely close to the standard cosmology at early epochs and adapt existing numerical codes to produce CMB anisotropy spectra. To find a FLRW model that matches as closely as possible the timescape expansion history, we have studied and compared a number of matching methods. We perform Markov Chain Monte Carlo analyses on the timescape model parameter space, and fit CMB multipoles 50 ≤ l ≤ 2500 to the Planck satellite data. Parameter fits include a dressed Hubble constant, H₀ = 61.0 kms ⁻¹Mpc⁻¹ (±1.3% stat)(±8% sys), and a present void volume fraction fᵥ₀ = 0.627 (±2.3% stat)(±13% sys). In the timescape model this value of fᵥ₀ means that the galaxy/wall observer infers an accelerating universe, where the apparent acceleration is due to gravitational energy gradients and clock rate differences rather than some dark energy. We find best fit likelihoods which are comparable to that of the best fit ΛCDM cosmology in the same multipole range.

In this thesis, we investigate the signatures of isocurvature initial conditions in the cosmic microwave background (CMB) through the temperature and polarization anisotropies, and in the large-scale structure distribution through the baryon acoustic oscillations (BAO). The first part of this thesis is a brief review of the standard cosmological model with its underlying linear cosmological perturbation theory. We supplement it with a general discussion on the initial conditions of the primordial fluctuations. In the third chapter, we review the evolution of the perturbations in the adiabatic model. We focus on the evolution of adiabatic perturbations in the photons and baryons from the epoch of initial conditions to the photon-baryon decoupling, as these determine the main features of the primary CMB anisotropies and of the baryon acoustic oscillations. The fourth chapter recalls the theory of the CMB anisotropies in the adiabatic model. We consider the perturbations from the last scattering surface and evolve them through the line of sight integral to get the adiabatic CMB power spectrum. We review the effect of different cosmological parameters on the adiabatic CMB temperature spectrum. In the fifth chapter, we investigate the observational signatures of the isocurvature perturbations in the CMB anisotropies. We first derive simple semi-analytic expressions for the evolution of the photon and baryon perturbations prior to decoupling for the four isocurvature regular modes and show that these modes excite different harmonics which couple differently to Silk damping and alter the form and evolution of acoustic waves. We study the impact of different cosmological parameters on the CMB angular power spectrum through the line of sight integral and find that the impact of the physical baryon and matter densities in isocurvature models differ the most from their effect in adiabatic models. In the last two chapters, we explore in detail the effect of allowing for small amplitude admixtures of general isocurvature perturbations in addition to the dominant adiabatic mode, and their effect on the baryon acoustic oscillations. The sixth chapter focuses on the distortion of the standard ruler distance and the degradation of dark energy constants due to the inclusion of isocurvature perturbations, while the seventh chapter discusses in more detail the sensitivity of BAO dark energy constraints to general isocurvature perturbations. We stress the role played by Silk damping on the BAO peak features in breaking the degeneracy in the peak location for the different isocurvature modes and show how more general initial conditions impact our interpretation of cosmological data in dark energy studies. We find that the inclusion of these additional isocurvature modes leads to a significant increase in the Dark Energy Task Force figure of merit when considered in conjunction with CMB data. We also show that the incorrect assumption of adiabaticity has the potential to substantially bias our estimates of the dark energy parameters. We find that the use of the large scale structure data in conjunction with CMB data significantly improves our ability to measure the contributions of different modes to the initial conditions. / Thesis (Ph.D.)-University of KwaZulu-Natal, Westville, 2012.

In this thesis, several theoretical concepts relating to the large-scale structure of the universe are presented. In particular, various aspects of the hierarchical scenario are investigated. The initial perturbation field and its early evolution are discussed in Chapter 3. Chapter 4 is concerned with two-point correlation functions for galaxies, clusters and super-clusters. In Chapter 5, some effects of using velocity as a distance measure are examined. In particular, it will be argued that caustics in redshift space are an almost inevitable feature of the hierarchical scenario. Chapter 6 concentrates on the possibity that quasar Ly-α absorption lines are redshift caustics.

This thesis describes an investigation into weak gravitational lensing, a unique and powerful astronomical tool for the study of dark matter on large scales. Lensing distorts background images, inducing correlations in the observed ellipticities of galaxies, and these correlations can be used to estimate many characteristics of the Universe. Key to all weak lensing studies is a reliable and unbiased method to detect weak lensing distortions from observed galaxy images that are contaminated by Earth and telescope-based shearing and smearing distortions. A new galaxy model-fitting technique is presented that has been developed in order to satisfy this requirement, which will also permit future signal-to-noise optimised measurements of weak lensing shear. Model-fitting provides a good alternative to the standard scite{KSB} method (KSB), and comparisons between the two techniques are drawn from an analysis of deep {it R} band imaging from the COMBO-17 survey, revealing strong evidence for the presence of bias in KSB galaxy shape measurement. With the galaxy model-fitting technique, an investigation into the effectiveness of the Oxford Dartmouth Thirty degree survey (ODT) for gravitational lensing studies is presented, resulting in the detection of weak gravitational lensing by large scale structure, or `cosmic shear', in 0.7 square degrees of the best seeing ODT images. One concern for all cosmic shear studies is that the weak lensing signal, manifest in the weakly correlated ellipticities of distant galaxies, is contaminated by the intrinsic alignment of close galaxy pairs, potentially induced during galaxy formation by physical interactions such as tidal forces. This contamination is investigated theoretically, through numerical simulations, and observationally, with an analysis of the COMBO-17 survey and the study of published results from the Red-sequence Cluster survey and the VIRMOS-DESCART survey, concluding that the intrinsic alignment effect is at the lower end of the range of theoretical predictions. The impact of intrinsic galaxy alignments on cosmological parameter estimation is investigated, with an analysis of the weak lensing results from the COMBO-17 survey. When marginalising over the observationally constrained intrinsic alignment signal, the amplitude of the matter power spectrum sigma_8 is reduced by ~0.03 to sigma_8(Omega_m / 0.27)^{0.6} = 0.71 pm 0.11, where Omega_m is the matter density parameter. With distance information from either spectroscopy or photometric redshifts, the down-weighting of nearby galaxy pairs in weak lensing analysis can be optimised to virtually eliminate the systematic errors in the shear signal arising from intrinsic galaxy alignments, leaving a much smaller, largely statistical error. This method is applied to the photometric redshift sample of the COMBO-17 survey. Weak lensing measurements from the forthcoming SuperNova/Acceleration Probe weak lensing survey (SNAP), and the Canada-France-Hawaii Telescope Legacy survey, are expected to be contaminated on scales >1 arcminute by intrinsic alignments at the level of ~ 1% and ~2% respectively. Division of the SNAP survey for lensing tomography significantly increases the contamination in the lowest redshift bin to ~7% and possibly higher. Removal of the intrinsic alignment effect by the downweighting of nearby galaxy pairs will therefore be vital for the lensing tomography studies of SNAP.

We quantify the structure and scale of the Universe using redshift surveys of galaxies and QSOs and observations of Galactic open star clusters. We obtain the galaxy power spectrum from the Durham/UKST Galaxy Redshift Survey. By comparing the shape of the observed power spectrum to the APM real space power spectrum, we quantify the size of the redshift space distortions and find β = Ω(^0.6)/b=0.60±0.35. We also apply counts-in-cells analysis to the Durham/UKST and Stromlo-APM Surveys and measure the skewness directly out to 20h(^-1)Mpc. We find that the skewness measured from CDM models can only be reconciled with that of galaxies if bias is non-linear. We make predictions for the clustering in the 2dF QSO Survey by constructing mock catalogues from the Hubble Volume N-body simulation, with geometry, selection function and clustering matching those expected in the completed Survey. We predict that the correlation function will be reliably measured out to ~ 1, 000h(^-1)Mpc and the power spectrum out to 500h(^-1)Mpc. We measure the power spectrum from the 2dF QSOs observed by January 2000 and find it has a shape of F ~ 0.1. We also find little evolution in the clustering amplitude as a function of redshift. We obtain constraints on the cosmo- logical parameters Ωn and β by combining results from modeling geometric distortions introduced into the clustering pattern due to inconsistent cosmological assumptions and results from the QSO-mass bias. Finally, we consider the scale of the Universe. We check the calibration of the Cepheid Period-Luminosity relation using U,B,V and K'band imaging of Galactic Open Clusters containing Cepheids and measure the distance modulus to the LMC to be 18.51 ±0.10. However, we find anomalous colour-colour diagrams for two clusters and suggest that the effects of metallicity may be greater than previously considered.

Cosmologists are interested in topological defects as a possible source for the primordial density perturbations which seeded structure formation through gravitational instability. In this thesis, the gravitational properties of various topological defects are studied in the context of low-energy string theory, a likely modification of Einstein gravity at the high energy scales prevalent in the early universe. We consider in turn global monopole, local monopole, global cosmic string and global texture defects, allowing for an arbitrary coupling of defects to the string theory dilaton. For global defects we find the following behaviour. If the dilaton is massless, this modification to general relativity generically destroys the global good behaviour of the monopole and cosmic string, making their spacetimes singular. For the texture non-singular spacetimes exist, but only for certain values of the matter-dilaton coupling, dependent on the gravitational strength of the defect; in addition, this non-singular behaviour exists only in a certain frame. In the case of a massive dilaton, the metric behaviour of these defects is similar to that found in Einstein gravity, though we find they generically induce a long-range dilaton cloud. For the local monopole, which we study only in the presence of a massless dilaton, a rich variety of behaviour is found. For particular parameter values the local monopole spacetime approximates that of an extremal dilaton black hole.

Typescript. / Thesis (Ph. D.)--University of Hawaii at Manoa, 1989. / Includes bibliographical references (leaves 710-719) / Microfiche. / xl, 719 leaves, bound ill. 29 cm

xii, 218 leaves / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.1978) from the Dept. of Mathematical Physics, University of Adelaide