With the wealth of data provided by modern imaging and redshift surveys, it has become essential to obtain measurements of galaxy properties in an automated fashion, and analyse them in a statistical manner. In this thesis we focus on two fundamental characteristics of the galaxy populations, their distributions in luminosity and their spatial clustering signal. We examine galaxies from the SDSS-II galaxy redshift survey, quantifying their distribution in luminosity as a function of rest-frame colour and visual morphology taken from the Galaxy Zoo project. In forming samples of the galaxies selected by colour, morphology and luminosity we observe that there are significant populations of both red spiral galaxies and blue early-type galaxies at redshifts of 0.01 < z < 0.2. To aid us in the description and analysis of these distributions we fit them with a parametric model, the well known Schechter function, in which we include parameterisations for the redshift evolution of absolute magnitude and number density. In comparing the results of fitting our various samples with the function we find that blue galaxies exhibit significantly different behaviour to spiral galaxies and that red galaxies exhibit significantly different behaviour to early-type galaxies. We then go on to measure the 2-point clustering statistics of the galaxies in order to explore the dependence of galaxy clustering bias on luminosity and colour. We fit our measurements of scale dependent galaxy clustering with several phenomenological models of galaxy bias. This allows us to describe how the large-scale bias and the transition to non-linear clustering behaviour depend on luminosity and colour. Our key result from this investigation is that red and blue galaxies exhibit significantly different clustering behaviour in both the amplitude of their large scale bias and their non-linear bias contributions at smaller scales. In conclusion we find that in order to extract the maximum amount of cosmological information from future surveys they must be planned and analysed with the understanding that galaxy clustering depends strongly on both luminosity and colour, and that galaxy morphology contains considerable information about a galaxies formation history, independent of its colour.

Stars light up galaxies that are the major building blocks of the Universe. Throughout this thesis we cover the analysis of stars and stellar populations to gain knowledge on the formation of galaxies and the evolution of the Universe. Understanding massive earlytype galaxies is key to understand mass assembly and the formation and evolution of galaxies in the Universe. The spectra of stellar populations carry a wealth of information regarding galaxy formation and evolution. Absorption lines are particularly useful as they are tracers of galaxy formation epoch and time-scale. Models of stellar populations are important tools for the analysis of galaxies. The accuracy of such models are crucial for the accuracy of the derived results. The first step in my thesis is therefore to improve upon current single stellar population models of absorption line indices. Calibration of the models with galactic globular cluster is crucial, since these are known to be close to single stellar populations. The main aim of the thesis is to apply the models to the analysis of earlytype galaxies and Type Ia supernovae (SN Ia) host galaxies. The main novelty of the stellar population models are new empirical calibrations of absorption line indices. These are based on the most comprehensive stellar library available to date MILES. The stellar spectra of this library have been carefully flux-calibrated. The models are therefore applicable to data without Lick index calibrations. Based on the new stellar population models we have developed a method for deriving element abundance ratios, including [O/Fe], [C/Fe], [N/Fe], [Mg/Fe], [Ca/Fe] and [Ti/Fe]. The method is applied to galactic globular clusters and we find the models to be well calibrated. The pattern of derived element abundance ratios show strong evidence for self-enrichment within globular clusters. The method for deriving element abundance ratios is then applied to �4000 SDSS early-type galaxies. The element abundance ratios [O/Fe], [Mg/Fe], [C/Fe] and [N/Fe] show strong correlations with stellar velocity dispersion. Using the derived trends of element abundance ratios we constrain the lower time-scale limit of star formation and star-burst components in massive early-type galaxies to �0.4 Gyr. Both in the globular cluster and early-type galaxy study we find that the heavy �-elements Ca and Ti scale with Fe rather than with the lighter �-elements O and Mg. This implies that a significant contribution from SN Ia to the enrichment of heavy �-elements is universally found and puts strong constraints on supernova nucleosynthesis and models of galactic chemical evolution. SN Ia as standard candles connect luminosity distance to redshift space to constrain cosmology. We derive stellar population parameters for a quality selected sample of 84 SN Ia host galaxies. We find that the stretch factor of SN Ia light-curves are mainly dependent on stellar population age, indicating that SN Ia progenitor mass is the main driver of the peak luminosities. We do not find any significant dependencies on host galaxy properties for the scatter in the luminosity-distance relationship after light-curve corrections. This implies that the derived cosmological parameters from SN Ia peak luminosities are robust.

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.

We present the cosmological analysis of 752 photometrically-classified Type Ia Supernovae obtained from the full Sloan Digital Sky Survey II Supernova Survey, supplemented with host-galaxy spectroscopy from the Sloan Digital Sky Survey III Baryon Oscillation Spectroscopic Survey. Our photometric-classification method is based on the supernovae typing technique of Sako et al. (2011), aided by host galaxy redshifts (0:05 < z < 0:55). SuperNova ANAlysis simulations of our methodology estimate that we have a Type Ia Supernovae typing efficiency of 70.8%, with only 3.9% contamination from Core-Collapse Supernovae. We demonstrate that this level of contamination has no effect on our cosmological constraints. We quantify and correct for our selection effects (e.g., Malmquist bias) using simulations. When fitting to a flat Λ Cold Dark Matter cosmological model, we find that our photometric sample alone gives Ωm = 0:24+0.07-0.05 (statistical errors only). If we relax the constraint on flatness, then our sample provides competitive joint statistical constraints on Ωm and Ωλ, comparable to those derived from the spectroscopically-confirmed three-year Supernova Legacy Survey. Using only our data, the statistics–only result favors an accelerating Universe at 99.96% confidence. Assuming a constant w Cold Dark Matter cosmological model, and combining with H0, Cosmic Microwave Background and Luminous Red Galaxies data, we obtain w = -0:96+0.10-0.10, Ωm = 0.29+0.02-0.02 and Ωk = 0.00+0.01-0.01 (statistical errors only), which is competitive with similar spectroscopically-confirmed Type Ia Supernovae analyses. Overall this comparison is reassuring, considering the lower redshift leverage of the Sloan Digital Sky Survey II Supernova Survey sample (z < 0:55) and the lack of spectroscopic confirmation used herein. These results demonstrate the potential of photometrically-classified Type Ia Supernovae samples in improving cosmological constraints, as well as promoting additional investigations of Type Ia Supernovae host galaxy correlation and possible Type Ia Supernovae lensing. We briefly discuss these issues in this thesis.

In 1998 astronomical observations of distant stars exploding at the ends of their lives led to the discovery that the expansion of the Universe is accelerating. This is likely to be caused by an intrinsic part of Einstein’s General Theory of Relativity known as the cosmological constant, but naturalness issues and the need to improve observational tests have motivated the study of alternative models of the Universe. The research in this thesis is part of ongoing efforts to pin down the cause of late-time acceleration by better understanding these alternatives and their signatures in cosmological observations. One such alternative is known as interacting dark energy and would be caused by additional matter in the Universe, as yet unknown to particle physics. This would interact with another unknown particle called dark matter that has been part of the standard model of cosmology since the 1970’s. The first part of this thesis contains a review of works on interacting dark energy and investigates a particular version of the model which had not been studied in detail before, placing recent observational constraints on its parameters. Another alternative to the cosmological constant is known as modified gravity, where General Relativity is extended by the addition of new degrees of freedom. Theories of modified gravity are mathematically related to some models of interacting dark energy and can appear very similar in cosmological observations. The second part of this thesis investigates the extent to which the two can be distinguished using current observational data.

In this work we explore the correspondence between the physical processes associated with inflationary models inspired by string theory and the subsequent non-Gaussian signatures imprinted in the primordial density perturbations. Specifically, we have chosen multiple-DBI inflation as a representative model to understand the effect of multiple-field dynamics and non-canonical kinetic terms on the resultant form of non-Gaussianity. We begin by introducing inflation as a mechanism to naturally lay down the initial conditions necessary for the hot big bang. Since the primordial density perturbations provide the best way to constrain inflationary models, we then review cosmological perturbation theory and provide the predictions of standard single-field, slow-roll inflation. Thereafter, we briefly review extensions to this model and introduce non-Gaussianity as a way to observationally discern between these otherwise degenerate scenarios. Thereafter, we study the effect of non-trivial sound speeds on local-type non-Gaussianity during multiple-field inflation. To this end, we use the δN formalism and a sum separable Hubble parameter to derive an analytic expression for the local-type non-linearity parameter in the two-field case, valid beyond slow variation. We find that non-trivial sound speeds can, in principle, curve the trajectory in such a way that significant local-type non- Gaussianity is produced. Deviations from slow variation, such as rapidly varying sound speeds, enhance this effect. To illustrate our results we consider inflation in the tip regions of two warped throats and find large local-type non-Gaussianity produced towards the end of the inflationary process. We then consider the equilateral contribution to the bi-spectrum by first calculating the full third-order action for the field fluctuations using the Arnowitt-Deser-Misner formalism. We then derive the corresponding three-point function for the field fluctuations at horizon-exit, to leading order in slow variation and small sound speeds. Thereafter, we again use the δN formalism and a separable Hubble parameter to present the combined local and equilateral contributions to the bi-spectrum of the curvature perturbation. We then revisit the case of inflation in two cutoff throats and find that the corresponding equilateral contribution is prohibitively large in this case. As an application of the above, we then explore further the parameter space of multiple- DBI inflation and, in particular, the dependence of large local-type non Gaussianity on initial conditions. To this end, we consider an alternative model of inflation in two cutoff throats that allows analytical solutions for the trajectories. We begin by considering the canonical limit of the model in which local-type non-Gaussianity is produced by the curvature of the potential. We find that such behaviour is highly dependent on the initial values of the fields. We then consider inflation in the tip regions of two cutoff throats and find that the production of large local-type non-Gaussianity through rapidly varying sound speeds is similarly dependent on initial conditions. Moreover, the equilateral contribution remains prohibitively large in such cases. Finally, we summarise our results and identify directions for future research, before providing a wider outlook for the inflationary paradigm in light of recent results from Planck.

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.