Modern cosmology has reached an important juncture, at which the ability to make measurements of unprecedented accuracy has led to conclusions that are a fundamental challenge to natural science. The discovery that, in our current best model, the dynamics of the Universe are completely dominated by unseen dark matter and dark energy can do little but completely alter the shape of physics research in the 21st Century. Unfortunately,much of our insight into these phenomenamust come from observations of visible matter alone; this raises serious problems, as the tracing of dark matter by visible matter is as yet poorly understood. Gravitational lensing offers strong prospects for probing the interwoven history of dark and visible matter, as mass in any form may be detected where it exists untraced by baryons. In this Thesis I describe advances made in the field of weak gravitational lensing, which constrains the properties of the matter distribution on cosmological scales using a statistical analysis of the coherent gravitational distortions of distant galaxy images. I summarize the development of gravitational flexion, a higher order extension to traditional weak lensing, and describe my work done to bring the study of flexion to a stage where it may be employed to make accurate cosmological measurements. I show how flexion is sensitive to matter structure on smaller physical scales than existing lensing techniques and, therefore, promises to shed new light upon key untested predictions of cosmological models if it can be measured to sufficient accuracy. I discuss the success of my efforts in this direction, and describe the issues to be encountered in the careful analysis of this subtle gravitational signal. This research has involved advances in many areas: the calculation of theoretical flexion predictions, the refinement of image analysis methods for accurate galaxy shape estimation, and the practical application of these new flexion techniques to extragalactic imaging data. The culmination of these efforts is a new maximum likelihood analysis of the galaxy-galaxy lensing signal in the Hubble Space Telescope Galaxy Evolution from Morphology and SEDs (GEMS) Survey, incorporating improvements and modifications necessary for the combination of flexion with traditional weak lensing measurements. The results of this work, and particularly the extent to which measurements of flexion provide extra cosmological insight, are discussed in detail. The conclusion is a summary of all that has been learned about the use of flexion as an accurate probe of cosmology, and a discussion of its prospects for answering some of the many questions that remain about dark matter. Within the next few year wide-area survey telescopes will begin imaging huge volumes of deep space, with the measurement of the gravitational lensing signal being given high priority in the analysis of these data. Within this context, the primary inquiry of this Thesis is the extent to which the application of flexion measurement techniques will help shed new light upon the unseen, and currently poorly understood, components of the Universe.

Many physical theories beyond the Standard Model predict time variations of basic physics parameters. Direct measurement of the time variations of these parameters is very difficult or impossible to achieve. By contrast, measurements of fundamental constants are relatively easy to achieve, both in the laboratory and by astronomical spectra of atoms and molecules in the early universe. In this work, measurements of the proton to electron mass ratio mu and the fine structure constant alpha are combined to place mildly model-dependent limits on the fractional variation of the quantum chromodynamic scale and the sum of the fractional variations of the Higgs vacuum expectation value (VEV) and the Yukawa couplings on time-scales of more than half the age of the universe. The addition of another model parameter allows the fractional variation of the Higgs VEV and the Yukawa couplings to be computed separately. Limits on their variation are found at the level of less than 5 x 10(-5) over the past 7 Gyr. A model-dependent relation between the expected fractional variation of a relative to mu tightens the limits to 10(-7) over the same time span. Limits on the present day rate of change of the constants and parameters are then calculated using slow roll quintessence. A primary result of this work is that studies of the dimensionless fundamental constants such as a and mu, whose values depend on the values of the physics parameters, are excellent monitors of the limits on the time variation of these parameters.

Na última década, o extraordinário progresso nas observações astronômicas (distâncias com supernovas (SNe Ia), espectros de potência da matéria e da radiação cósmica de fundo (RCF), determinação do brilho de aglomerados de galáxias, etc.) aliado com importantes desenvolvimentos teóricos, transformaram a Cosmologia numa das fronteiras mais excitantes da ciência contemporânea. Nesta tese, diferentes testes observacionais são utilizados para vincular alguns cenários cosmológicos acelerados (com e sem energia escura), todos eles definidos no contexto teórico da Relatividade Geral. Inicialmente, para uma grande classe de modelos com decaimento do vácuo, investigamos os vínculos provenientes da existência de objetos velhos em altos redshifts. No modelo de Chen e Wu generalizado, encontramos que o limite para o parâmetro livre descrevendo a taxa do decaimento do vácuo é 0,21 < n < 0,81. Este resultado descarta o modelo de Chen e Wu original (n=2) e também o modelo de concordância cósmica, LCDM (n=0). Além disso, quando incluímos o fluido bariônico em nossa análise do modelo de Wang e Meng, obtemos para seu parâmetro livre um limite inferior, epsilon > 0,231, um valor em desacordo com estimativas independentes baseadas em SNe Ia, RCF e o brilho de Raios-X de aglomerados. Propusemos também um teste estatístico com base nas idades estimadas para uma amostra de 13 galáxias velhas em altos redshifts. Através de uma análise conjunta envolvendo as idades das galáxias e as oscilações acústicas dos bárions (BAO), vinculamos o valor da constante de Hubble no contexto do modelo LCDM plano. Considerando um tempo de incubação adotado por diferentes autores, obtemos h=0,71±0,04 (1 sigma), um resultado de acordo com observações independentes baseadas em Cefeidas (obtidas com o Hubble Space Telescope) e outras estimativas mais recentes. Outro resultado interessante foi obtido através de uma análise termodinâmica para uma classe de modelos com interação no setor escuro (matéria escura-energia escura). Contrariamente ao que se pensava até então, encontramos que a termodinâmica permite que a matéria escura decaia em energia escura, contanto que ao menos uma das componentes possua um potencial químico não-nulo. Como complemento, mostramos que, para um termo de interação específico, dados de SNe Ia, BAO e RCF favorecem o decaimento da matéria escura com ~ 93% de confiança estatística. Investigamos também o comportamento do redshift de transição em diferentes cosmologias, com e sem energia escura, e mostramos que essa quantidade pode ter uma variação extrema dependendo do modelo cosmológico subjacente. Finalmente, discutimos também um novo modelo cosmológico cuja aceleração em baixos redshifts é determinada pela criação de partículas da matéria escura fria. O modelo representa uma redução do setor escuro, isto é, não tem energia escura, contém apenas um parâmetro livre e satisfaz os vínculos de Supernovas do tipo Ia tão bem quanto o modelo LCDM padrão. / In the last decade, the extraordinary progress of the astronomical observations (distances with supernovas, matter and cosmic background radiation (CBR) power spectrum, X-ray surface brightness of galaxy clusters, etc) associated with important theoretical developments turned Cosmology one of the most exciting frontiers of contemporary science. In this thesis, different observational tests are used to constrain several cosmological accelerating scenarios (with and without dark energy), all of them defined in the theoretical framework of General Relativity. Initially, for a large class of decaying vacuum models, we investigate the constraints provided by the existence of old high redshift objects. In the model proposed by Chen and Wu, we find that the limit for the free parameter describing the decay rate of the vacuum fluid is 0.21 < n < 0.81. This result ruled out the original Chen and Wu model (n = 2) and also the cosmic concordance model, LCDM (n = 0). Further, when we include the baryonic fluid in our analysis of the Wang and Meng model, we find for its free parameter a lower bound, epsilon > 0.231, a value in disagreement with independent estimates based on SNe Ia, CMB (shift parameter) and the X-ray surface brightness of galaxy clusters. We also propose a new cosmological statistical test based on the estimated ages of 13 old high redshift galaxies. By performing a joint analysis involving the ages of the galaxies and the baryon acoustic oscillations (BAO) probe, we constrain the value of the Hubble parameter in the context of the flat LCDM model. For an incubation time adopted by different authors, we find h = 0.71 ± 0.04 (1 sigma), a result in agreement with independent observations based on Cepheids (obtained with the Hubble Space Telescope) and other recent estimations. Another interesting result has been derived from a thermodynamic analysis for a class of models endowed with interaction in the dark sector (dark matter and dark energy). In contrast with some results appearing in the literature, we show that the decaying of cold dark matter into dark energy is not forbidden by thermodynamics, provided that the chemical potential of one component is different from zero. As a complement, we also show (for a specific term describing the interaction) that this kind of decaying is favored by SNe Ia, BAO and CMB data with ~ 93% of statistical confidence. We also investigate in detail the behavior of the transition redshift for different cosmologies (with and without dark energy). It is found that such a quantity may have an extreme variation that depends on the underlying cosmological model. Finally, we also discuss a new cosmological model whose acceleration at low redshifts is determined by the creation of cold dark matter particles. The model represents a reduction of the dark sector, that is, it has no dark energy, contains only one free parameter and satisfies the Supernovae type Ia constraints with the same precision of the standard LCDM model.

Neste trabalho, estudamos modelos cosmológicos em que a energia escura foi tratada como um campo de matéria que interage com a matéria escura. Três modelos distintos foram considerados. O primeiro trata tanto a matéria escura fria quanto a energia escura como fluidos perfeitos. O termo de interação entre eles é dado por uma expressão com origem fenomenológica que postulamos existir na equação de balanço entre esses dois fluidos. Dadas as equações no universo plano de Friedmann-Robertson-Walker (FRW), pudemos escrever uma versão covariante para as equações de balanço. Com isso, as equações de balanço em um universo de FRW perturbado linearmente foram obtidas. Isso, por sua vez, permitiu que a estabilidade das equações diferenciais obtidas fosse estudada. O segundo modelo tem origem em modelos de f(R). Esses modelos propõem uma generalização da Relatividade Geral ao considerar a ação da gravidade como um funcional do escalar de Ricci, R. Através de uma transformação conforme, foi possível reinterpretar os modelos de f(R) como modelos em que um campo escalar canônico, que representa a energia escura, interage com os campos da matéria. Através do princípio da ação, obtivemos as equações de movimento e o tensor de energia-momento para nosso sistema. Com o campo escalar sendo interpretado como um fluido perfeito, pudemos, por fim, obter equações de balanço entre fluidos perfeitos tanto no nível de fundo quanto no universo perturbado linearmente. O terceiro modelo começa com a lagrangiana, em um espaço-tempo de FRW, de um campo escalar canônico, que representa a energia escura, e um campo fermiônico de spin-1/2, que representa a matéria escura. Um termo de interação de Yukawa entre esses campos foi postulado existir na lagrangiana. Novamente através do princípio da ação, obtivemos as equações de movimento e o tensor de energia-momento para esses campos. Essas equações de movimento puderam, por fim, ser reescritas como equações de balanço entre fluidos perfeitos tanto no nível de fundo quanto no universo perturbado linearmente. / In this work we studied cosmological models in which the dark energy was treated as a field of matter that interacts with dark matter. Three different models were considered. The first one treats both the cold dark matter and the dark energy as perfect fluids. The interaction term between them is given by a expression with phenomenological origin that we postulated to exist in the balance equations between these two fluids. Given the equations in the flat Friedmann-Robertson-Walker (FRW) universe, we wrote a covariant version of the balance equations. Thus, the balance equations in a linearly perturbed FRW universe were obtained. This, in turn, allowed the stability of the obtained differential equations to be studied. The second model comes from f(R) models. These models propose a generalization of General Relativity by considering the action for gravity as a functional of the Ricci scalar, R. Through a conformal transformation, it was possible to reinterpret the f(R) models as models in which a canonical scalar field, which represents the dark energy, interacts with matter fields. Through the principle of least action, we obtained the equations of motion and the energy-momentum tensor for our system. With the scalar field being interpreted as a perfect fluid, we obtained equations of balance for perfect fluids at both the background level and in the linearly perturbed universe. The third model starts with the Lagrangian, in a FRW space-time, of a canonical scalar field, which represents the dark energy, and of a fermionic field of spin-1/2, which represents the dark matter. A Yukawa interaction term between these fields was postulated to exist in the Lagrangian. Again, through the principle of least action, we obtained the equations of motion and the energy-momentum tensor for these fields. These equations of motion could then be rewritten as balance equations for perfect fluids at both the background level and in the linearly perturbed universe.

In this thesis we go beyond the standard cosmological LCDM model and study the effect of an interaction between dark matter and dark energy. Although the LCDM model provides good agreement with observations, it faces severe challenges from a theoretical point of view. In order to solve such problems, we first consider an alternative model where both dark matter and dark energy are described by fluids with a phenomenological interaction given by a combination of their energy densities. In addition to this model, we propose a more realistic one based on a Lagrangian density with a Yukawa-type interaction. To constrain the cosmological parameters we use recent cosmological data, the CMB measurements made by the Planck satellite, as well as BAO, SNIa, H0 and Lookback time measurements. / Nesta tese vamos além do modelo cosmológico padrão, o LCDM, e estudamos o efeito de uma interação entre a matéria e a energia escuras. Embora o modelo LCDM esteja de acordo com as observações, ele sofre sérios problemas teóricos. Com o objetivo de resolver tais problemas, nós primeiro consideramos um modelo alternativo, onde ambas, a matéria e a energia escuras, são descritas por fluidos com uma interação fenomenológica dada como uma combinação das densidades de energia. Além desse modelo, propomos um modelo mais realista baseado em uma densidade Lagrangiana com uma interação tipo Yukawa. Para vincular os parâmetros cosmológicos usamos dados cosmológicos recentes como as medidas da CMB feitas pelo satélite Planck, bem como medidas de BAO, SNIa, H0 e Lookback time.

Neste trabalho discutimos um modelo baseado em teoria de campos para descrever a energia escura, no qual ela é representada por uma partícula ultra-leve situada em um mínimo metaestável de um potencial. Mostramos que a energia escura neste modelo decai em matéria escura durante o tempo de vida do universo, amenizando o problema da coincidência. / In the present work we discuss a field theory model in which dark energy is described by ultra-light particle situated at a metastable minimum of a potential. We show that dark energy in this model decays into dark matter during a time scale corresponding to the age of the universe, alleviating the coincidence problem.

Li Baojiu = 宇宙学和新物理学的交叉领域 / 李宝九. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 93-99). / Text in English; abstracts in English and Chinese. / Li Baojiu = Yu zhou xue he xin wu li xue de jiao cha ling yu / Li Baojiu. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Some Basic Conceptions in Cosmology --- p.2 / Chapter 1.1.1 --- "The Big Bang, Hubble's Law" --- p.2 / Chapter 1.1.2 --- The Cosmological Principle and Robertson-Walker Metric --- p.3 / Chapter 1.1.3 --- The Cosmological Redshift --- p.4 / Chapter 1.1.4 --- The Friedmann Equations --- p.4 / Chapter 1.2 --- Big Bang Nucleosynthesis --- p.5 / Chapter 1.3 --- Dark Energy --- p.9 / Chapter 2 --- "Branes, Varying Constants and BBN" --- p.16 / Chapter 2.1 --- A Brief Introduction to Theories Involving Extra Dimensions --- p.17 / Chapter 2.1.1 --- The Kaluza-Klein Theory --- p.18 / Chapter 2.1.2 --- Large Extra Dimensions --- p.19 / Chapter 2.1.3 --- Warped Extra Dimensions --- p.22 / Chapter 2.1.4 --- Universal Extra Dimensions --- p.24 / Chapter 2.1.5 --- Cosmology in a Brane World --- p.27 / Chapter 2.2 --- BBN and Varying Constants in Brane Models --- p.29 / Chapter 2.2.1 --- The Low Energy Effective Action in Brane Models --- p.30 / Chapter 2.2.2 --- BBN with a Varying Higgs VEV --- p.34 / Chapter 2.3 --- Numerical Results --- p.38 / Chapter 2.4 --- Discussion and Conclusions --- p.47 / Chapter 3 --- "Universal Extra Dimensions, Varying Constants and BBN" --- p.49 / Chapter 3.1 --- Introduction --- p.50 / Chapter 3.2 --- The Low Energy 4-Dimensional Effective Actions --- p.50 / Chapter 3.3 --- Radion Dependence of Fundamental Constants --- p.54 / Chapter 3.4 --- Variations of Quantities Relevant For BBN Calculation --- p.57 / Chapter 3.4.1 --- Neutron-proton Mass Difference --- p.57 / Chapter 3.4.2 --- Weak Interaction Rates --- p.58 / Chapter 3.4.3 --- Expansion Rate of the Universe --- p.58 / Chapter 3.4.4 --- Nuclear Reaction Rates --- p.59 / Chapter 3.5 --- Numerical Results --- p.64 / Chapter 3.6 --- Discussion and Conclusions --- p.70 / Chapter 4 --- Dark Energy as a Signature of Extra Dimensions --- p.74 / Chapter 4.1 --- Introduction --- p.75 / Chapter 4.2 --- The Underlying Higher Dimensional Theory --- p.75 / Chapter 4.3 --- The Cosmic Evolution in Different Eras --- p.79 / Chapter 4.3.1 --- The Blazing Era --- p.79 / Chapter 4.3.2 --- The Radiation Dominated Era --- p.83 / Chapter 4.3.3 --- The Matter Dominated Era --- p.84 / Chapter 4.4 --- A Realistic Cosmology --- p.85 / Chapter 4.5 --- Discussions and Conclusions --- p.92 / Bibliography --- p.93

Intensity mapping (IM) is a new observational technique to survey the large-scale structure of matter using emission lines, such as the 21 cm emission line of atomic hydrogen (HI) and the rotational lines of the carbon monoxide molecule (CO). Sensitive radio surveys have the potential to detect the HI power spectrum at low redshifts (z &lt;1) in order to constrain the properties of dark energy and massive neutrinos. Observations of the HI signal will be contaminated by instrumental noise and, more significantly, by astrophysical foregrounds, such as the Galactic synchrotron emission, which is at least four orders of magnitude brighter than the HI signal. In this thesis, we study the ability of the Generalized Needlet Internal Linear Combination (GNILC) method to subtract radio foregrounds and to recover the cosmological HI signal for HI IM experiments. The GNILC method is a new technique that uses both frequency and spatial information to separate the components of the observed data. For simulated radio observations including HI emission, Galactic synchrotron, Galactic free-free, extragalactic point sources and thermal noise, we find that it can reconstruct the HI plus noise power spectrum with 7.0% accuracy for 0.13 &lt;z &lt;0.48 (960 - 1260 MHz) and l &lt;400. In this work, GNILC is also applied to a particular CO IM experiment: the CO Mapping Array Pathfinder (COMAP). In this case, the simulated radio observations include CO emission, Galactic synchrotron, Galactic free-free, Galactic anomalous microwave emission, extragalactic point sources and thermal noise. We find that GNILC can reconstruct the CO plus noise power spectra with 7.3% accuracy for COMAP phase 1 (l &lt;1800) and 6.3% for phase 2 (l &lt;3000). In both cases, we have 2.4 &lt;z &lt;3.4 (26 - 34 GHz). In this work, we also forecast the uncertainties on cosmological parameters for the upcoming HI IM experiments BINGO (BAO from Integrated Neutral Gas Observations) and SKA (Square Kilometre Array) phase-1 dish array operating in auto-correlation mode. For the optimal case of BINGO with no foregrounds, the combination of the HI angular power spectra with Planck results allows w to be measured with a precision of 4%, while the combination of the BAO acoustic scale with Planck gives a precision of 7%. We consider a number of potentially complicating effects, including foregrounds and redshift dependent bias, which increase the uncertainty on w but not dramatically; in all cases the final uncertainty is found to be less than 8% for BINGO. For the combination of SKA-MID in auto-correlation mode (total-power) with Planck, we find that, in ideal conditions, w can be measured with a precision of 4% for the redshift range 0.35 &lt;z &lt;3 (350 - 1050 MHz) and 2% for 0 &lt;z &lt;0.49 (950 - 1421 MHz). Extending the model to include the sum of neutrino masses yields a 95% upper limit of less than 0.30 eV for BINGO and less than 0.12 eV for SKA phase 1, competitive with the current best constraints in the case of BINGO and significantly better in the case of SKA.

Neste trabalho analisamos algumas consequências físicas de uma cosmologia acelerada com interação no chamado setor cósmico escuro (energia escura + matéria escura fria). A componente de energia escura é representada por uma densidade de energia do vácuo que varia com o tempo e cuja lei de decaimento tem a seguinte forma: $\\Lambda = \\Lambda_0 + {3\\alpha}/{a^{2}}$, onde $\\Lambda_0$ é o termo de vácuo usual, $\\alpha$ é um parâmetro livre e $a(t)$ o fator de escala. Nesse contexto discutimos a tensão existente entre os dados de Supernovas (que preferem um Universo fechado, $\\Omega_{\\kappa} > 0$) e os dados da radiação cósmica de fundo que favorecem um Universo espacialmente plano ($\\Omega_{\\kappa} = 0$). Considerando que o termo variável simula uma curvatura (pois ambos possuem a mesma dependência no fator de escala), mostramos que sua contribuição atua no sentido de aliviar a tensão SNe Ia-CMB existente no modelo de concordância cósmica padrão ($\\Lambda CDM$, $\\alpha=0$). O modelo resolve o problema da idade do Universo e para $a>>1$, tal como ocorre com $\\Lambda CDM$, também evolui para um estágio de Sitter. O parâmetro $\\alpha$ é limitado através de uma análise estatística conjunta envolvendo dados de Supernovas, CMB ({\\it shift parameter}) e oscilações acústicas dos bárions (BAO). Separando o termo de vácuo em duas componentes ($\\Omega_{\\Lambda 0}$ e $\\Omega_{\\alpha 0}$) um teste $\\chi^{2}$ fornece os seguintes valores para o modelo plano: $\\Omega_{m0} = 0,27 \\pm 0,02$, $\\Omega_{\\Lambda 0} = 0,74 \\pm 0,02$ e $\\Omega_{\\alpha 0} = -0,01 \\pm 0,03$. / In this work we analyze some physical consequences of an accelerating cosmology endowed with interaction in the cosmic dark sector (dark energy + cold dark matter). The dark energy component is represented by a time-dependent vacuum energy whose decay law has the following form: $\\Lambda = \\Lambda_0 + {3\\alpha}/{a^{2}}$, where $\\Lambda_0$ is the standard vacuum term, $\\alpha$ is a free parameter and $a(t)$ is the scale factor. In this context we discuss the existing tension between Supernovas (SNe Ia, which prefer a closed Universe, $\\Omega_{\\kappa} > 0$) and the cosmic background radiation (CMB) data (which are favoring a spatially flat Universe, $\\Omega_{\\kappa} = 0$). By considering that the variable $\\Lambda$-term mimics a curvature (since both terms have the same dependence on the scale factor), we show that its contribution helps to alleviate the tension SNe Ia-CMB existing in the standard cosmic concordance model. The present model solves the age of the Universe problem and for $a>>1$, it also evolves to a de Sitter model as occur with the $\\Lambda CDM$ scenario. The contribution of the $\\alpha$ parameter is limited through a joint statistical analysis involving Supernovas, CMB ({\\it shift parameter}) and baryon acoustic oscillations (BAO). By separating the variable vacuum term in two components ($\\Omega_{\\Lambda 0}$ e $\\Omega_{\\alpha 0}$), a $\\chi^{2}$ test furnishes the following values for the free parameters of the flat model: $\\Omega_{m0} = 0,27 \\pm 0,02$, $\\Omega_{\\Lambda 0} = 0,74 \\pm 0,02$ and $\\Omega_{\\alpha 0} = -0,01 \\pm 0,03$.

One of the most pressing, modern cosmological mysteries is the cause of the accelerated expansion of the universe. The energy density required to cause this large scale opposition to gravity is known to be both far in excess of the known matter content, and remarkably smooth and unclustered across the universe. While the most commonly accepted answer is that a cosmological constant is responsible, alternatives abound. This thesis is primarily concerned with such alternatives; both their theoretical nature and observational consequences. In this thesis, we will dedicate Chapter 1 to a brief review on the fundamentals of general relativity, leading into the basics of theoretical cosmology. Following this we will recall some of the key observations that has lead to the standard CDM cosmology. The standard model has well known problems, many of which can be answered by the theoretical ideas of inflation. In Chapter 2 we explore these ideas, including a summary of classical field theory in the context of cosmology, upon which inflation is based. This also serves as the groundwork for Chapter 3, where the varied models of dark energy (and their motivations) are discussed - many of which are also reliant on field theory (such as quintessence). These notions are combined in a model described in Chapter 4, where we describe our own addition to a scenario that unifies dark energy and inflation. This addition - involving a coupling of the inflation field to an additional one - alter the way reheating takes place after inflation, removing some of the shortcomings of the original proposal. The analysis is extended in Chapter 5, to include the effect of quantum corrections. There we show that although a cursory analysis indicates a coupling between quintessence and some other field does not necessarily give rise to dangerously large quantum corrections, provided the effects of decoupling are taken into account. We move on in Chapter 6 to examine the basics of cosmological perturbation theory, and derive the general equations of motion for density and velocity perturbations for a system of fluids, allowing for the exchange of energy-momentum. We make use of this in Chapters 7 and 8, were we examine the growth of structure in a universe where energy is exchanged between dark matter and dark energy. In particular, in Chapter 7 we see that a particular form of the interaction can lead to an instability in the early universe, and we derive the condition for this to be the case. In Chapter 8, we discuss how a similar interaction can lead to a mimicry of modified gravity, and relate this directly to cosmological observations. Finally we summarise our conclusions and discuss avenues of future research in Chapter 9.