Cosmology, intended as the study of the origin and evolution of the Universe and its components, has advanced from being a philosophical discipline to a data-driven science. Much of this progress was achieved in the last few decades thanks to the wealth of cosmological data from Earth and space-based experiments. The abundance of observational constraints has considerably narrowed the space for theoretical speculation, to the point that now most of the cosmological community agrees on a standard model of cosmology. A crucial assumption of this model is that the structure observed in the Universe, such as planets, stars and galaxies, can be ultimately traced back to tiny density perturbations in the early Universe. Therefore, a huge theoretical and experimental effort is being made by cosmologists and particle physicists to gain insight of the mechanism of generation of these primordial fluctuations, which remains still largely unknown. The bispectrum of the cosmic microwave background (CMB) has been recently recognised as a powerful probe of this mechanism, as it is sensitive to the non-Gaussian features in the seed fluctuations. To access this information, however, it is crucial to model the non-linear evolution of the CMB between the formation of the initial fluctuations and its observation, which results in the emergence of an intrinsic bispectrum. The main purpose of this thesis is to quantify the intrinsic bispectrum and compute the bias it induces on the primordial signal. To do so, we develop SONG, a new and efficient code for solving the second-order Einstein-Boltzmann equations, and use it to estimate the intrinsic CMB non-Gaussianity arising from the non-linear evolution of density perturbations. The full calculation involves contributions from recombination and less tractable ones from terms integrated along the line of sight. We investigate the bias that this intrinsic bispectrum implies for searches of primordial non-Gaussianity. We find that the inclusion or omission of certain line of sight terms can make a large impact. When including all physical effects but lensing and time-delay, we find that the contamination from the intrinsic bispectrum generally leads to a small bias in the estimates of non-Gaussianity, which is good news for the prospect of using cosmic microwave background data to probe primordial non-Gaussianity. The intrinsic non-Gaussianity can be searched for directly, using the predicted signal as a template; our calculations suggest this signal is just beyond what is possible with the Planck CMB survey, with a signal-to-noise rising to unity only for an angular resolution of `max = 3000.

The advent of wide-field galaxy surveys with high quality imaging provides an opportunity to map the dark matter distribution in large parts of the visible Universe. However, the available probes of the large-scale structure have distinct properties. In particular, galaxies are a high resolution but biased tracer of mass, while weak lensing avoids such biases but, due to low signal-to-noise ratio, has poor resolution. After reviewing the applications of maps in cosmology, I investigate the relation between the Fourier phases of cosmological fields. By considering Gaussian random fields, I take some steps in describing the statistics of phase difference. Then I consider some simple models of realistic cosmological fields galaxies and weak gravitational lensing. I find that a linear bias evolving in redshift leads to a scale independent phase difference, whereas shot noise and stochasticity lead to a scale dependent phase difference. I investigate reconstructing the projected density field using the complementarity of weak lensing and galaxy positions. I propose a maximum probability reconstruction of the 2D lensing convergence with a likelihood term for shear data and a prior on the Fourier phases constructed from the galaxy positions. By considering only the phases of the galaxy field, the method evades the unknown value of the bias and allows it to be calibrated by lensing on a mode-by-mode basis.

In this work we present a new full spectral fitting code called FIREFLY. It is a c2-minimisation code that obtains thousands of spectral fits in order to build probability distribution functions of stellar population properties, and includes an innovative method to treat dust attenuation. We use the code to determine galaxy properties, including age, metallicity, stellar mass and dust extinction, of over 2 million galaxy spectra, both from point-source and from resolved galaxy surveys, using modern high-resolution stellar population models. We analyse the results to assess the redshift evolution of galaxy properties, and the importance of their internal processes. We test a set of stellar population models based on three stellar libraries to assess the systematic effects of changing model ingredients and provide a detailed assessment of degeneracies in the models, in all stages of the thesis. After introducing the central concepts in galaxy evolution and astrophysics, we describe the advancements of stellar population models and their use in the derivation of galaxy properties. We then give a detailed overview of the landscape of full spectral fitting and its application to observational data. We describe the motivation, features and function of FIREFLY, performing careful calibration on a set of mock galaxies and globular clusters. We also very carefully assess the degeneracies in model spectra and measure the uncertainties from applying a full spectral fitting approach to optical data. We apply FIREFLY to two observation point-source surveys with millions of galaxy members: the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7), and SDSS Data Release 9, the galaxy data of which is called the Baryon Oscillation Spectroscopic Survey (BOSS). We present the full star formation histories of all of the galaxies in the surveys and important subsamples within them. We use the derived galaxy properties as the calibrator for combining these surveys into one large survey across redshifts 0.0 < z < 0.8. This enables us to assess the redshift evolution of the most luminous and passive galaxies across both samples. Significantly, we use FIREFLY in the first scientific publication of SDSS-IV, for the MaNGA Integral Field Unit survey. We retrieve stellar population maps and radial profiles from high spatial resolution prototype observations of 18 galaxies, encompassing thousands of individual spectra. Our analysis gives detailed measurements of the precision to which one can recover stellar population gradients and resolved maps as a function of observational conditions and stellar population model ingredients, paving the way for future work both in MaNGA and other spatial galaxy surveys.

The very early universe is where we expect the observed primordial perturbations in the cosmic microwave background to have originated. In this thesis we study isocurvature field fluctuations during inflation and ekpyrotic contraction as sources of the primordial curvature perturbations. We start by introducing concepts of modern cosmology followed by an overview of early universe cosmology. After, we introduce perturbation theory and how to compute perturbations from early universe models. After reviewing all fundamental concepts necessary for this thesis, we estimate largescale curvature perturbations from isocurvature fluctuations in the waterfall field during hybrid inflation, in addition to the usual inflaton field perturbations. The tachyonic instability at the end of this inflation model leads to an explosive growth of super-Hubble scale perturbations, but they retain the steep blue spectrum characteristic of vacuum fluctuations in a massive field during inflation. We extend the usual δN formalism to include the essential role of small fluctuations when estimating the large-scale curvature perturbation. The following two chapters study perturbations within the curvaton proposal. Firstly, we consider how non-Gaussianity of the primordial density perturbation and the amplitude of gravitational waves from inflation can be used to determine parameters of the curvaton scenario for the origin of structure. We show that in the simplest quadratic model, where the curvaton evolves as a free scalar field, measurement of the bispectrum relative to the power spectrum, fNL, and the tensor-to-scalar ratio can determine both the expectation value of the curvaton field during inflation and its dimensionless decay rate relative to the curvaton mass. We show how these predictions are altered by the introduction of self-interactions. In the following chapter, we then characterise the primordial perturbations produced due to both inflaton and curvaton fluctuations. We show how observational bounds on non-linearity parameters and the tensor-scalar ratio can be used to constrain curvaton and inflaton parameters. The final research presented in this thesis, considers a simple model of cosmological collapse driven by canonical fields with exponential potentials. We generalise the two-field ekpyrotic collapse to consider non-orthogonal potentials and give the general condition for isocurvature field fluctuations to have a slightly red spectrum of perturbations as required by current observations. However a red spectrum of fluctuations implies that the two-field ekpyrotic phase must have a finite duration and requires a preceding phase which sets the initial conditions for what otherwise appears to be a fine-tuned trajectory in the phase space. We end this thesis with some concluding remarks and comments on possible future work.

In this work I address two of the big questions in modern astrophysics; the role of environment as a driver of galaxy evolution, and the the role of mass in star formation and stellar population evolution. I use one of the most powerful tools available to the astrophysical community, large-scale galaxy spectroscopy, to contribute towards the answers to these dilemmas. I construct a data analysis pipeline based on the public codes gandalf and pPXF to extract gas and stellar dynamics, emission line statistics, absorption line indices and stellar population parameters from these galaxy spectra. I test and calibrate this pipeline against existing results for the Sloan Digital Sky Survey Data Release 7, and find it to provide accurate measurements. I use the emission line results from this to probe the dependence of star formation and ionisation characteristics on stellar mass, local environment and global environment in the Galaxy AND Mass Assembly survey. I find that mass is the main driving factor behind the presence of star formation and determining different ionisation sources, and see a trend with increasing mass from star forming objects to those hosting active galactic nuclei via composites of the two. Local density plays a role only at the highest densities, and is considerably less significant than mass; global environment is found to have negligible impact. This suggests that star formation quenching is primarily a mass-driven process, with active galactic nucleus feedback being a likely candidate for the environment independent process involved in our sample. I stack objects together from the Sloan Digital Sky Survey III: Baryon Oscillation Spectroscopic Survey in order to produce high-signal-to-noise spectra for the purpose of absorption line measurement and the subsequent modelling of stellar population parameters. I use this to investigate the dependence of age, metallicity and α/Fe on mass (using stellar velocity dispersion as a proxy for dynamical mass) and redshift. I find that light-averaged age, metallicity and α/Fe all increase with velocity dispersion, which are predictions of the downsizing paradigm, where the least massive galaxies form their stars later, over more extended timeframes and less effciently than more massive galaxies. Age is also seen to increase with redshift, which is simply the result of everything in the Universe getting older, whilst I see no evidence of metallicity or α/Fe changing with lookback time. Investigating how galaxies age when compared to the Universe, I find that more massive galaxies appear to age faster than the Universe whilst less massive galaxies age slower. I hypothesise that this is due to the different star formation histories of galaxies with differing masses, and test this by compiling models with varying stellar histories and comparing them to our observations. I find that as mass decreases, I require more extended periods of star formation that peak more recently. At the high-mass end, the relationship between the most massive bins is best reproduced by a passively evolving population whose stars formed at higher redshift than I observe. This is a clear result of downsizing, and sets tough restrictions on future models of galaxy formation and evolution.

Reconstructing an estimate of linear Baryon Acoustic Oscillations (BAO) from an evolved galaxy field has become a standard technique in recent analyses. By partially removing non-linear damping caused by bulk motions, the real-space baryon acoustic peak in the correlation function is sharpened, and oscillations in the power spectrum are visible to smaller scales. In turn, these lead to stronger measurements of the BAO scale. Future surveys are being designed assuming that this improvement has been applied, and this technique is therefore of critical importance for future BAO measurements. A number of reconstruction techniques are available, but the most widely used is a simple algorithm that de-correlates large-scale and small-scale modes approximately removing the bulk-flow displacements by moving the overdensity field. The initial work presented in this thesis shows the practical development of a reconstruction algorithm which is extensively tested on the mock catalogues created for the two Baryon Oscillation Spectroscopic Survey (BOSS) Date Release 11 samples covering redshift ranges 0:43 < z < 0:7 and 0:15 < z < 0:43. The practical implementation of this algorithm is tested, looking at the efficiency of reconstruction as a function of the assumptions made for the bulk-flow scale, the shot noise level in a random catalogue used to quantify the mask and the method used to estimate the bulk-flow shifts. The reconstruction algorithm developed in Chapter 2 is applied to 5 different galaxy survey data sets. The algorithm was used directly to create the reconstructed catalogues used to extract the cosmological distance measurements published in [3, 4, 5, 6], the results and cosmological implications are presented. The efficiency of reconstruction is also tested against external factors including galaxy density, volume and edge effects, and the impact for future surveys is considered. The results of this work are published here. The measurement of linear redshift space distortions apparent in the observed distribution of matter provides information about the growth of structure and potentially provides a way of testing general relativity on large scales. The last chapter of the thesis presents a model of the reconstructed redshift space power spectrum in resummed Lagrangian perturbation theory which is a new result. The goal of the work is to create a reconstruction algorithm that enhances the linear redshift space distortion signal measured from an evolved galaxy distribution analogous to the improvement seen in the BAO signal post-reconstruction.

Inflation was introduced to the Big Bang model of the universe as a method to solve the problems associated with this model. It also gave an explanation for the small scale inhomogeneities observed in the universe today. Since the concept was introduced, more complex models inflation have been postulated as time has gone on. However the amount of information available to measure the feasability of all these models has not grown at the same rate. Very high precision measurements are now making it possible to start getting significant measurements of parameters measuring how non-Gaussian the distributions of perturbations from the inflation models are. These measurements have mostly been done using third order statistics,i.e. the bispectrum. The work presented in this looks at how good a measurement Planck will be able to make of non-Gaussian parameters using fourth-order statistics, i.e. the trispectrum. In particular this work looks at models which have a second mode in addition to the standard adiabatic mode of the curvature perturbation, the isocurvature mode. These modes can be generated by models where there is more than one field present during inflation. Both these modes could be non-Gaussian, which gives rise to 17 parameters that can measure non-Gaussianity using the trispectrum. The aim of this work is to determine how good a measurement Planck could make of these parameters, especially considering they are not independent of each other. This work is presented in the context of determing bounds for model parameters for different inflation models.

Robust measurements of the large scale structure of the universe allow for precise characterisation of its low redshift behaviour and its late time accelerating expansion rate. In particular, Baryon Acoustic Oscillations (BAO) provide a standard ruler with which to measure the expansion rate, whilst Redshift Space Distortions (RSD) allow for tests of General Relativity on cosmological scales. In recent years many surveys have used these probes to investigate the nature of dark energy across a wide range of redshifts with increasing accuracy, culminating in a recent 1% measurement of the BAO scale by Anderson et al. (2014b). Current measurements point towards a consensus cosmological model where dark energy is described only by a Cosmological Constant. However, much of the parameter space available for dark energy models remains unexplored, a point that future surveys such as Euclid (Laureijs et al., 2011), DESI (Levi et al., 2013), LSST (Ivezic et al., 2008) and SKA (Maartens et al., 2015) will attempt to rectify. This thesis presents work that further confirms the consensus cosmological model using a set of new BAO and RSD measurements at low redshift, whilst also providing tools and techniques to aid in the analysis of next generation datasets. To begin with, a new code for fast dark matter simulation is presented that can be used to generate large ensembles of accurate mock galaxy catalogues for use in estimating the statistical and systematic errors inherent within large scale structure measurements. The accuracy and speed of this code are tested, where it is found that the new code can reproduce the real-space 2- and 3-point dark matter clustering from a full non-linear N-Body simulation to within 2% and 5% on all scales of interest to BAO and RSD measurements. However each simulation can be run 3 orders of magnitude faster than the corresponding non-linear N-Body run. Several new features are also implemented that will be of use in constructing mock galaxy catalogues for next generation surveys. This code, the algorithms involved and its testing are published in Howlett et al. (2015b) New measurements of the BAO and RSD signals in a low redshift galaxy sample drawn from the Sloan Digital Sky Survey Data Release 7 are also presented, along with their subsequent cosmological constraints. The simulation code above is first used to generate a set of mock galaxy catalogues based on the low redshift sample, before the sample and simulations are analysed using the most up-to-date BAO and RSD analysis methods. The procedure for generating the mock catalogues is tested and the clustering of the simulations is found to match that of the data extremely well, even down to scales of 5 h−1 Mpc. Using the mock catalogues, the BAO and RSD fitting methods are checked for robustness before being used on the data set to obtain a new set of constraints on the expansion rate, equation of state of dark energy and growth rate of structure. In particular, the new BAO measurement completes the low redshift BAO distance ladder and improves current BAO and CMB constraints on the equation of state of dark energy by ⇠ 15%, to w0 = −1.010 ± 0.081. This work is published in Ross et al. (2015) and Howlett et al. (2015a). Finally, a new optimal method for estimating the covariance matrix of the two point clustering of matter is presented, based on a combination of analytic and simulation approaches. This new method can reproduce the covariance matrix stimated from the mock galaxy catalogues simulations used in the rest of this work very well on small scales, in a regime where theoretical estimates of the covariance matrix are extremely difficult to obtain accurately. The benefit of this method is that only simulations that are a fraction of the volume of the full mock galaxy catalogues are required, which in turn means fewer particles are needed to reach the same mass resolution and more simulations (and hence a more precise estimate of the covariance matrix) can be obtained for the same computational cost. The combination of this work and the new fast simulation code presents a much more practical and cost effective way of estimating the covariance matrix.

Cosmology aims to study the origin, composition and evolution of the entire Universe. The standard model for cosmology, called ΛCDM , represents a good fit to most of the observations we have, but it is a phenomenological model with no strong theoretical foundation, so one of the biggest challenges in cosmology (but important for the entire physics) will be to understand if this is the correct model (and so try to find a theoretical framework for it) or if a model with some sort of “new” physics will take place as the standard one. From the theoretical point of view there are several attempts to solve open problems in cosmology, such as the origin of the Universe and the nature of dark energy; their solution could shed some light on profound and interesting questions potentially revolutionising our understanding of nature. Important data revealing the nature of dark energy will be provided by forthcoming and planned galaxy surveys, that will reach a high precision in their measurements. Data available in the next years will allow us to constrain much better the cosmic expansion history, the geometry of the Universe and the growth of structures within it. For this reason, in this thesis we focused on observational tests of one of the key aspects of a cosmological model, the growth of structures; this allowed us to perform tests of cosmological models and General Relativity. We performed studies of the evolution of growth and clustering of cosmological structures and the evolution of the gravitational potential, comparing effects that depend on them against observations coming from various datasets. In particular, in Chapter 2 we test the growth of structures and their clustering using Redshift-Space Distortions (RSD), developing a new methodology to carefully analyse large scale spectroscopic galaxy surveys; we implement and test a practical application of the wide-angle formalism and then we investigate the significance of different systematics that affect measurements of large scale RSD. In Chapter 3 we use the Integrated Sachs-Wolfe (ISW) effect to test cosmological models to search for possible deviations from the ΛCDM model and then to test a model for the evolution of low frequency radio sources. In Chapter 4 we forecast cosmological measurements it will be possible to obtain using forthcoming radio surveys, using different probes such as the auto-correlation of radio sources, the ISW effect, the Cosmic Magnification and a joint analysis, in order to show how they can be used to test deviations from the standard cosmological constant and General Relativity models.

In this thesis, we present a comparison of the evolution of the massive galaxies in the 7.8Gyr since redshift z=1 to the evolution predicted from galaxy formation models. Observing the most massive galaxies in the Universe at high redshift is challenging due to their red colours, owing to both their intrinsically red Spectral Energy Distributions (SEDs) and their redshift. In Chapter 1, We produce a method using catalogue-level data to produce matched aperture photometry for the SDSS and UKIDSS surveys in order to extend the wavelength coverage of a sample of galaxies in order to improve the precision with which models can be fitted to photometric data for these high redshift galaxies. Our matched photometry has consistent colours with those of the full processing of SDSS+UKIDSS images performed by the GAMA survey, and produces magnitudes within ∼0.1 magnitudes of the GAMA photometry for all galaxies. This is reduced to within 0.04 magnitudes when all blended sources are excluded. We compute stellar masses by fitting a Maraston et al. (2009) LRG model to both our derived photometry and that of the GAMA processing, and find that our photometry’s best fit stellar masses are within ∼0.2 dex of that which comes from the GAMA photometry, demonstrating that the method is consistent with that of a full processing, and that it is possible to quickly compute matched photometry for large area surveys of complimentary wavelength coverage. This is of vital importance for upcoming surveys e.g. DES, VISTA, EUCLID etc. Fitting Stellar Population Models to galaxy photometry is a widely used technique in order to convert from observables (colours, magnitudes) to physical properties (mass, absolute magnitude, age). In spite of their widespread use, the optical and Near Infrared (NIR) properties of stellar population models are still subject to debate. Two of the most commonly used models are those of (Maraston, 2005) (M05) and (Bruzual & Charlot, 2003) (BC03), which can differ greatly in the NIR due to the M05 models’ inclusion of the TP-AGB phase, which was neglected for BC03 models. We explore the ability of these models to reproduce measured optical+NIR properties of galaxies in Chapter 3. We produce matched optical+NIR photometry for the subsample of the galaxies surveyed by Zibetti et al. (2013) (Z13) which lie within the UKIDSS imaging area in an attempt to reproduce the findings of Z13, who conclude that their optical and NIR spectroscopy is better fit by models from Bruzual & Charlot (2003) than similar models from Maraston et al (2005). We compare the observed optical+NIR Spectral Energy Distributions (SEDs) to those of BC03 and M05 models, as well as the approximate Z13 NIR fluxes. Z13 found that M05 models fitted to the optical data and extrapolated into the NIR displayed excess flux in the NIR relative to the data, and BC03 models are better at reproducing the data. However, we show that our data is consistent with both sets of models, and on average brighter in the NIR than that of Z13. We also compare the strength of spectral features in the optical to rest frame optical and optical-NIR colours, and show that our set of Composite Stellar Population (CSP) models agree well with data, with a preference for the M05 models, showing the validity of using these models on massive galaxies. A measurement of the Stellar Mass Function (SMF) of galaxies is a powerful tool in detecting evolution of the galaxy population. With a statistically complete sample of a galaxy population down to a given stellar mass, it is possible to calculate a statistically complete SMF down to this mass. Comparison of the shape of this SMF to that of a similar sample over a different redshift interval allows the evolution of galaxies over this redshift interval to be calculated, in order to determine whether these galaxies are forming stars, merging or simply passively evolving. For this purpose, in 4 compute matched SDSS+UKIDSS photometry for the AA omega KIDSS SDSS (AUS) survey. This is a 145.416 deg² area survey of Luminous Red Galaxies (LRGs) from redshift z∼0.5 to z∼1 located within Stripe 82. We fit this photometry to a Maraston et al. (2009) Luminous Red Galaxy (LRG) template to give stellar masses, and scale masses according to the magnitude difference between the matched photometry and the SDSS model photometry in order to produce “total” stellar masses. We produce a volume-weighted SMF for the survey, and find that our SMF is consistent with the Maraston et al. (2013) SMF from the BOSS survey, meaning that the most massive galaxies in the universe are evolving passively from z=1 to the present day, which is a challenge to hierarchical models of galaxy formation. Comparison of observed SMFs to those produced by galaxy formation models is a method of testing the ability of the models to reproduce the evolution displayed by the real galaxy population. This is therefore a test of the physics included within the models, with the level of agreement between the simulation and the real galaxy SMF being indicative of whether the modelling has incorporated all the processes in action in the real universe. In order to test the ability of the state of the art semi analytical models of Henriques et al. (2013) (H13 hereafter), we compare SMFs of the simulated galaxies to those of the AUS and BOSS surveys in Chapter 5. The H13 galaxies were tailored via the application of both the AUS and BOSS colour and magnitude cuts, and SMFs calculated within lightcones of the same area as the surveys in order to compare equal volumes. Our findings extend the conclusions of Maraston et al. (2013), namely that the most massive galaxies in the simulations are not sufficiently massive to agree with the observed galaxy population at this redshift. By extending this analysis to redshift z∼1, we can confirm that the discrepancy is larger at higher redshift, with the difference between the most massive galaxies in the simulations and those observed being log(ΔM/M⊙) ≃0.2 at z≃0.6–0.7, whereas going beyond this to the range z≃0.7–1 the difference becomes log(ΔM/M⊙) ≃0.25, as can be seen in Figure 5.6, which demonstrates that the simulations are failing to either form, or assemble, the mass quickly enough to reproduce the observations. Instead, the simulations continue to assemble mass through to low redshift at a higher rate than is seen in the galaxy SMF. These discrepancies may indicate that the physics of the simulations is not fully accounting for the real processes in the Universe,and that we do not yet have a model capable of reproducing the galaxy population in the real universe. Clearly semi analytical galaxy simulations need to be modified in order to reproduce the observations, before being further challenged by upcoming spectroscopic surveys of galaxies at redshifts as high as z=2 eg. eBoss, DESI.