The observed accelerated expansion of the universe is one of the big issues of modern cosmology. One possible way of understanding it is by modifying General Relativity so that gravity is weaker at large scales. Higher-dimensional models that offer infrared modifications of gravity provide just that. Braneworld models are a subclass of these, where standard matter is confined to a p dimensional brane living in a p+d dimensional “bulk” space. Gravitons, however, can access the extra d dimensions. The Dvali-Gabadadze-Porrati(DGP) model realizes this by having a 4D brane embedded in 5D space-time. By including an induced gravity term in the action, standard 4D gravity is recovered at small scales, whereas at large scales gravity is 5D. This model is particularly interesting because of its phenomenology, namely the existence of two cosmological branches, one of which, called the self-accelerating branch, exhibits late time cosmic acceleration even when no matter is present in the brane. However, such cosmologies, at the linear level, have been found to be plagued by ghost instabilities that cause a catastrophic instability of space-time thus automatically excluding the model as a viable explanation of reality. In this thesis, after a brief introduction to the covered topics, we start by going beyond linearity to see if non-linear interactions might change previous results on the presence of the ghost. We did this for a cosmological background and, in the process, derived the equations that form the basis of structure formation tests in the DGP model. Our analysis however, proves the validity of the linearized solutions and, thus, the presence of the ghost. We then used a numeric algorithm to solve the full 5D set of dynamical equations for the scalar perturbations in the DGP model. Our numeric solutions are the basis for comparison of the ghost-free normal branch with cosmological observations. Whereas there seems to be no way of avoiding the ghost problem in the self-accelerating branch of the DGP model, a generalization of it that removes the symmetry across the brane had been shown to be ghost-free in a flat background while retaining some form of late-time acceleration (given the name of stealth acceleration) in certain limits. We study the spectrum of perturbations for a de Sitter background in the same setup. Our analysis showed that the only way to avoid a ghost is precisely to have Minkowski branes. Finally, yet another generalization of the DGP model, in this case a generalization of its 4D effective action called the Galileon model, is shown to possess the self-accelerating solutions. We present an extension of the Brans-Dicke theory by adding a third order Galileon term to the Brans-Dicke action that appears in the 4D effective theory of DGP gravity. An analysis of our model shows the presence of self-acceleration for a certain region of it’s parameter space, without any ghost or tachyonic instabilities.

The use of Baryon Acoustic Oscillations (BAO) as a standard ruler in the 2-point galaxy clustering signal has proven to be an excellent probe of the cosmological expansion. With the abundance of good quality galaxy data predicted for future large sky surveys, the potential to conduct precision cosmology using clustering analyses is immense. Many of the next generation sky surveys, including the Dark Energy Survey (DES), the Panoramic Survey Telescope and Rapid Response System (PanStarrs), and the Large Synoptic Survey Telescope (LSST), will utilise photometric redshift estimation techniques, which will make it possible to probe wider and deeper regions of the Universe than spectroscopic redshift surveys in an equivalent amount of time. The use of photometric techniques to estimate galaxy redshifts however, induces errors on inferred radial distances. Consequently, the amplitude of the power spectrum and correlation function is reduced in the radial direction by this smoothing. In this regime, precise measurements of the BAO signal will be difficult. Because of this, there is an urgent need to obtain a better understanding of exactly how photometric redshift uncertainties affect 3D clustering analyses, and to investigate alternative clustering analysis techniques that may be used in future experiments. In this thesis, I investigate the systematic effects arising in the projected correlation function due to redshift-space distortions, and introduce a new binning scheme to eradicate the problem. I also consider the level of systematic uncertainty induced in realistic measurements of the 3D correlation function from conflicting photometric redshift estimation techniques, and highlight a requirement for empirical test results to be incorporated into model predictions of the anisotropic correlation function for future surveys. Finally, I collate my results to make predictions about how BAO can be optimally used in future photometric redshift experiments like the DES.

The subject matter of this thesis is the formation of large-scale structure in the universe. Most of the study has dealt with the non-linear evolution of cosmological uctuations, focusing on the scalar sector of perturbation theory. The period of transition between the radiation era and the matter era has been largely examined, extending the already known linear results to a nonstandard matter model and to a non-linear analysis. The obtained second order solutions for the matter uctuations variables have been used to find the skewness of the density and velocity distributions, an important statistical estimator measuring the level of non-Gaussianity of a distribution. In the context of cosmological perturbations, a complete Post-Newtonian (1PN) treatment is presented with the aim of obtaining a set of equations suitable in particular for the intermediate scales. The final result agrees with both the non linear Newtonian theory of small scales and the linear general relativistic theory of large scales. Analyzing the limiting cases of our approach to 1PN cosmology, we have clarified the link between the Newtonian theory of gravity and General Relativity. This work is the result of the agreement signed by the Department of Physics, University of Roma Tor Vergata and the Institute of Cosmology and Gravitation, University of Portsmouth, United Kingdom in the formal context of the co-tutela project. The chapters 5, 6 and 7 are the themes of two articles in preparation, that will be shortly submitted: "How the universe got its skewness" - M. Bruni, I.Milillo, K.Koyama; "Post-Newtonian Cosmology" - I. Milillo, D.Bertacca, M. Bruni

In the last two decades astronomers carried out a large number of galaxy surveys tuned towards the study of galaxy formation and evolution. With the ever improving technology, increasing telescope sizes of ground-based telescopes and the development of space-based telescopes it has become possible to detect galaxies at a time when the Universe was only a few hundred million years old. However, for the majority of galaxies a detailed spectroscopic analysis is not possible due to their distance and limited telescope time. Thus, many surveys rely on photometric data alone to help unveil the properties of galaxies. One of the most important areas of study within galaxy formation and evolution is the analysis of the galaxy stellar population parameters as these can provide us with information about the star formation histories of galaxies and when and possibly how they assembled their mass. A popular approach in the literature is the fitting of synthetic spectral energy distributions inferred from stellar population modelling to the multi-wavelength photometry of galaxies. However, this approach comes with a large number of fitting parameters all of which are essentially user-dependent and will bias the result in one way or another. The aim of this thesis is to investigate the accuracy and efficiency of spectral energy distribution fitting as derivation technique for the galaxy physical properties, such as age, stellar mass, dust reddening, etc., as a function of the fitting parameters, such as star formation histories, age grids, metallicity, initial mass function, dust reddening, reddening law, filter setup and wavelength coverage and stellar population model, and to find the setup of parameters that recovers the properties best. In particular, we investigate in detail the dependence of the derived properties on the assumed wavelength coverage and exact filter setups. Mock galaxies with known properties serve as test particles for this exercise. The synthetic spectral energy distributions used in this thesis are based on the Maraston (2005) stellar population models. Literature results which investigate similar problems are obtained using the models of Bruzual & Charlot (2003). Firstly, the fitting is carried out under the assumption that galaxy redshifts are known mimicking surveys for which galaxy redshifts are derived spectroscopically. Then we study the case in which the redshift is not known and needs to be determined alongside the galaxy physical properties which is the case for most photometric surveys. In general, we find that - using normal template star formation histories as widely used in the literature - ages and stellar masses of star-forming galaxies are underestimated, reddening and star formation rates are overestimated. This is due to a mismatch in star formation history and the overshining effect. The addition of the rest-frame near-IR appears to be crucial for the derivation of robust results. For aged galaxies with little or no on-going star formation we find that a setup covering a wide range of star formation histories and metallicities works best when the fit is carried out excluding dust reddening. For high redshift star-forming galaxies we find that a new type of star formation history (inverted-� models which start forming stars at high redshift) recovers stellar masses and star formation rates best. The parameters of truly passive galaxies are much better determined. In order to ease the comparison of literature data that was analysed with different fitting parameter setups we provide scaling relations for the transformation of stellar masses between different setups. Our results concerning the importance of the wavelength coverage in the fitting are particularly useful for the planning of future surveys and observation proposals. We apply our findings from the study of mock galaxies to various samples of real galaxies which cover different redshift ranges and galaxy types. We derive the stellar population properties for a sample of star-forming galaxies at z ∼ 2 from the GOODS-S survey using inverted-� models (with high formation redshifts) and show that the obtained dust reddening and star formation histories are in excellent agreement with those derived from other methods. We also show how the wrong set of fitting parameters can lead to unrealistically young ages, low stellar masses and high star formation rates which are a pure artefact from the fit. Furthermore, we study a sample of low redshift, predominantly passive galaxies from the SDSS-III/BOSS survey for which we use the spectral model of Maraston et al. (2009) that is tuned to the needs of this particular type of galaxies. We find that BOSS galaxies are mostly passive, old and massive at each redshift in the range 0 < z < 0.7. Finally, we complement the study of SDSS-III/BOSS galaxies by deriving stellar masses for the SDSS-I/II galaxies in a similar fashion. We conclude that the simultaneous derivation of stellar population properties of galaxies from spectral energy distribution fitting is difficult but that these properties can be very well derived provided the right setup and wavelength coverage are used in the fitting. We also conclude that more work is needed to better match star formation histories of aged galaxies with little on-going star formation in order to improve estimates of stellar population parameters.

Over the last few decades enormous progress has been made in the study of the Universe and we are now entering the age of precision cosmology, with numerous upcoming high precision surveys expected to provide us with an incredible wealth of information. Observational data is usually interpreted once assumptions about the underlying cosmology are made. One of those commonly made assumptions is that the Universe is homogeneous and istropic, which observations seem to indicate is the case on very large scales. We develop a class of exact inhomogeneous solutions to general relativity for dust and a cosmological constant with which we can model a line of sight with arbitrary matter distribution; far away from this line of sight the solutions tend towards a standard homogeneous model of the Universe. This class of solutions is very well suited to model the effects of inhomogeneities along the line of sight on cosmological observations. We find that the effects of the inhomogeneities on the relation between distance and redshift are small if one imposes that the inhomogeneities along the line of sight average to the background density. Using compensated structures of several shapes and sizes, we find the deviations from the distance redshift relation to be below 1%. However, as soon as the lines of sight are not completely compensated larger deviations are found. We investigate this effect further and compare several exact solution to general relativity and perturbative approaches. The results from the three exact solution are very similar and indicate that uncompensated lines of sight can result in distance – redshift relations very different to the homogeneous ones. For small fluctuations we find that the complete linear analysis agrees with the results from exact solution but weak lensing predictions do not. The expansion rates along lines of sight which are not compensated are different than in the background which causes the large deviations in the distance – redshift relation. We find that void regions expand faster than in the background, but can they expand fast enough to explain the observed cosmic acceleration? However, on smaller scales such as galaxies and groups of galaxies this is clearly not the case. With the precision of observations increasing to unprecedented levels, is it still justifiable to make the assumption that the Universe is homogeneous on all scales even though we know that this is not the case on most scales? Much of this thesis is dedicated to this question. To answer this question from the exact solutions point of view we develop an inhomogeneous solution to general relativity for a single fluid with a constant equation of state parameter in the background. Within this solution we investigate the expansion properties of compensated regions and void regions. We find that compensated regions expand as the background and find that void regions do expand faster than the background but cannot cause cosmic acceleration. The physical mechanisms at work during the early Universe are not very well understood yet, but the hope is that through the data provided by future high precision surveys we might be able to constrain some of the theories. In particular constraints on the levels of primordial non-Gaussianity will be a powerful discriminator between theories. Therefore we investigate the growth of matter inhomogeneities to second perturbative order in a concordance cosmology and find the dependence of the density fluctuations on primordial non-Gaussianities. We also show how Newtonian and purely general relativistic non-linear effects enter into the second order density fluctuations. This understanding is essential in extracting information about primordial non-Gaussianties from the distribution of large scale structure today. Lastly, we analysed a proposed way of probing cosmic expansion by using the well studied Alcock-Paczynski effect in the dynamics of galaxy pairs. We studied the dynamics of galaxy pairs in an N-body simulation and found that once several cuts are made on the selection of the galaxy pairs, including isolation criteria, mass cuts and separation cuts, there might be a possibility of using pairs with such properties as cosmic tracers. Modelling of the velocities of the galaxies due their mutual attraction and local densities needs to be done first though to remove systematic errors in the observations.

Forthcoming wide field weak lensing surveys, such as DES and Euclid, present the possibility of using lensing as a tool for precision cosmology. This means exciting times are ahead for cosmological constraints for different gravity and dark energy models, but also presents possible new challenges in modelling, both non-standard physics and the lensing itself. In this thesis I look at how well DES and Euclid will be able to discriminate between different cosmological models and utilise lensing’s combination of geometry and growth information to break degeneracies between models that fit geometrical probes, but may fail to fit the observed growth. I have focussed mainly on the non-linear structure growth regime, as these scales present the greatest lensing signal, and therefore greatest discriminatory power. I present the predicted discriminatory power for modified gravities models, DGP and f(R), including non-linear scales for DES and Euclid. Using the requirement that modified gravities must tend to general relativity on small scales, we use the fitting formula proposed by Hu & Sawicki to calculate the non-linear power spectrum for our lensing predictions. I demonstrate the improved discriminatory power of weak lensing for these models when non-linear scales are included, and show that not allowing for the GR asymptote at small scales can lead to an overestimation in the strength of the constraints. I then parameterise the non-linear power spectrum to include the growth factor, and demonstrate that even including these extra parameters there is still more power in a full non-linear analysis than just using linear scales. I then present non-linear weak lensing predictions for coupled dark energy models using the CoDECS simulations. I obtain predictions for the discriminatory power of DES and Euclid in distinguishing between ΛCDM and coupled dark energy models; I show that using the non-linear lensing signal we could discriminate between ΛCDM and exponential constant coupling models with β0 ≥ 0.1 at 99.994% confidence level with a DES-like survey, and β0 ≥ 0.05 at 99.99994% confidence level with Euclid. I also demonstrate that estimating the coupled dark energy models’ non-linear power spectrum, using the ΛCDM Halofit fitting formula, results in biases in the shear correlation function that exceed the survey errors. I then present weak lensing predictions for DES and Euclid, and the CMB temperature power spectrum expected for Planck for fast transition adiabatic unified dark matter models. I demonstrate that in order to constrain the parameters in this model a high and low redshift observational probe is required. I show that for a ΛCDM fiducial, Planck could constrain zt > 5 at a 95% confidence level, and DES and Euclid could constrain the maximum time the transition can take to < 5 × 10−6/H0 at a 95% confidence level. Finally I look at a full general relativistic model of lensing. I adopt the use of a Lemaitre-Tolman-Bondi model, with and without pressure, to model an overdensity in an expanding background in a continuous spacetime. I use this to examine how the modelling of intermediate scales affects lensing quantities, and whether, as has been suggested recently, the cosmological constant has a direct effect on the lensing observables.

Cosmology motivated by string theory has been studied extensively in the recent literature. String theory is promising because it has interesting features such as unifying gravity, electromagnetic, weak and strong nuclear forces. However, even the energy scale of the experiments at the Large Hadron Collider (~TeV) is too low to detect any strong evidence for string theory. The energy scale of inflation can be above ~ 109 TeV. Therefore, it is expected to find some signature of string theory in cosmology. String theory predicts ten space-time dimensions. In the brane world scenario, our four dimensional Universe is confined onto the higher dimensional object called the Brane in the ten dimensional space time. The Dirac-Born-Infeld (DBI) inflation is based on this idea. DBI inflation predicts a characteristic statistical feature in the Cosmic Microwave Background (CMB) temperature anisotropies. In this thesis, we study the predictions of the DBI inflation models on the CMB temperature anisotropies. In chapter 1, the idea of inflation in the early stage of the Universe is introduced after explaining why we need inflation in addition to the standard Big Bang scenario. At the end of this chapter, we introduce the CMB observables that quantify the statistical properties of the CMB anisotropies. In chapter 2, we introduce the cosmological perturbation theory for general multi-field inflation including DBI inflation. After studying the linear perturbation theory, we introduce the higher order perturbations that produce the non- Gaussianities. The analytic formulae for the CMB observables that are valid in cases with the effective single field dynamics around horizon crossing are summarised at the end of this chapter. In chapter 3, the idea of DBI inflation is introduced. Some analytic predictions for the CMB observables are given in a simple single field DBI inflation model. After introducing the microphysical constraint that excludes the single field DBI inflation, we show that this constraint can be significantly relaxed if the trajectory in the field space is bent in multi-field DBI inflation models. In chapter 4, we study the specific two-field DBI inflation model with a potential that is derived in string theory. The potential contains only the leading order term ignoring all other possible corrections in string theory. After studying how curves in the trajectories in the field space affect the CMB observable, we show that this model is excluded by observation in the regime where the analytic formulae introduced in chapter 2 are valid. At the end of this chapter, we discuss the cases where we cannot use the analytic formulae and discuss possible implications In chapter 5, we study the two-field DBI inflation model with a potential that has the essential feature of the potential obtained with other corrections in addition to the leading term in string theory. In this model, inflation is driven by the motion of a D3 brane along the radial direction and at later times instabilities develop in the angular directions. It is shown that it is actually possible to satisfy the microphysical constraint with a turn in the trajectory in the field space. However, this particular choice of potential is excluded with the constraint on the local type non-Gaussianity by the latest CMB observations of the PLANCK satellite. We discuss the future perspective of DBI inflation models in the last chapter.

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.