>Magister Scientiae - MSc / The growth rate of large-scale structure is a key probe of gravity in the accelerating Universe. Standard models of Dark Energy within General Relativity predict essentially the same growth rate, whereas Modified Gravity theories without Dark Energy predict a different growth rate. Redshift-space distortions lead to anisotropy in the power spectrum, and extracting the monopole and quadrupole allows us to determine the growth rate and thus test theories of gravity. We investigate redshift-space distortions in the intensity maps of the 21cm emission line of neutral hydrogen (HI) in galaxies after the Epoch of Reionization: HI intensity mapping delivers very accurate redshifts. We first use the standard approach based on the Fourier power spectrum. Then we explored an alternative approach, based on the spherical-harmonic angular power spectrum. Fisher forecasting was used to make predictions of the accuracy with which MeerKAT will measure the growth rate parameter, via the proposed MeerKAT Large Area Synoptic Survey (MeerKLASS). Then we extend the forecasts to consider the planned HI intensity mapping survey in Phase 1 of the Square Kilometre Array. These forecasts enable us to predict at what level of accuracy General relativity and various alternative theories could be ruled out.

Nós investigamos o raio de turnaround, a distância do centro da estrutura cósmica até a casca que está se descolando do fluxo de Hubble em um dado tempo, no contexto do modelo de colapso esférico, tanto em Relatividade Geral e em Gravidade Modificada, em particular no cenário f(R) chamado de modelo de Hu-Sawicki. O próximo passo foi investigar a relação entre este raio e a massa de virial de estruturas cósmicas no contexto do modelo LCDM e no modelo f(R) de gravidade modificada. / We investigate the turnaround radius, the distance from the center of the cosmic structure to the shell that is detaching from the Hubble flow at a given time, in the context of the spherical collapse model, both in General Relativity and in modified gravity, in particular f(R) scenarios -- namely the Hu-Sawicki model. The next step was to investigate the relationship between that radius and the virial mass of cosmic structures in the context of LCDM model and in an f(R) model of modified gravity.

Late-time cosmic acceleration is one of the most interesting unsolved puzzles in modern cosmology. The explanation most accepted nowadays, dark energy, raises questions about its own nature, e.g. what exactly is dark energy, and implications to the observations, e.g. how to handle fine tuning problem and coincidence problem. Hence, dark energy evolution through cosmic history, together with its equation of state, are subjects of research in many current experiments. In this dissertation, using Markov Chain Monte Carlo sampling, we try to constrain the evolution of the dark energy equation of state in a nearly model-independent approach by combining different datasets coming from observations of baryon acoustic oscillations, cosmic chronometers, cosmic microwave background anisotropies and type Ia supernovae. We found no strong evidence that could indicate deviations from LCDM model, which is the standard model in cosmology accepted today. / A aceleração cósmica atual é um dos mais interessantes enigmas não resolvidos da cosmologia moderna. A explicação mais aceita hoje em dia, a energia escura, levanta questões acerca de sua própria natureza, como o que é exatamente a energia escura, e as implicações para as observações, por exemplo como lidar com o problema do ajuste fino e o problema da coincidência. Por isso, a evolução da energia escura durante a história cósmica, juntamente com sua equação de estado, são objetos de pesquisa em inúmeros experimentos atuais. Nesta dissertação, usando amostragem por cadeias de Markov de Monte Carlo, tentamos restringir a evolução da equação de estado da energia escura em uma abordagem quase independente de modelo ao combinar diferentes conjuntos de dados provenientes de observações de oscilações acústicas de bárions, cronômetros cósmicos, anisotropias da radiação cósmica de fundo e supernovas tipo Ia. Não encontramos evidências fortes que pudessem indicar desvios do modelo LCDM, o qual é o modelo padrão aceito hoje na cosmologia.

Nós investigamos o raio de turnaround, a distância do centro da estrutura cósmica até a casca que está se descolando do fluxo de Hubble em um dado tempo, no contexto do modelo de colapso esférico, tanto em Relatividade Geral e em Gravidade Modificada, em particular no cenário f(R) chamado de modelo de Hu-Sawicki. O próximo passo foi investigar a relação entre este raio e a massa de virial de estruturas cósmicas no contexto do modelo LCDM e no modelo f(R) de gravidade modificada. / We investigate the turnaround radius, the distance from the center of the cosmic structure to the shell that is detaching from the Hubble flow at a given time, in the context of the spherical collapse model, both in General Relativity and in modified gravity, in particular f(R) scenarios -- namely the Hu-Sawicki model. The next step was to investigate the relationship between that radius and the virial mass of cosmic structures in the context of LCDM model and in an f(R) model of modified gravity.

O impacto que estruturas algébricas podem exercer em teorias físicas e bem ilustrado pela Mecânica Quântica, onde os números complexos são inquestionavelmente a escolha mais adequada para desenvolver a teoria. A Relatividade Geral pseudo-complexa avalia a possibilidade da interação gravitacional assumir sua descrição mais natural quando construída tendo como base os números pseudo-complexos, que consistem em uma das três possibilidades de números complexos abelianos com uma unica unidade imaginária. Esse conjunto numérico e dotado de elementos não nulos cujo produto e zero, tais números recebem o nome de zeros generalizados ou divisores de zero. A presença de zeros generalizados permite a introdução de um princípio variacional modificado do qual um termo adicional, ausente na Relatividade Geral, emerge nas equações de campo. Esse termo adicional e interpretado como uma energia escura, cuja origem física está relacionada com flutuações no vácuo. A inclusão desse efeito e legítima pois flutuações no vácuo a priori devem gravitar como qualquer outra forma de energia. Das equações de campo podemos resumir a principal ideia conceitual da teoria, na Relatividade Geral pseudo-complexa massa não apenas curva o espaçotempo como também e capaz de alterar a estrutura do espaço-tempo ao redor da massa. As diferenças com relação a Relatividade Geral se manifestam em situações físicas extremas, no regime de campos gravitacionais intensos. Como aplicação analisamos sob o ponto de vista teórico um objeto compacto exótico composto por matéria escura fermiônica. / The impact that algebraic structures can exert on physical theories is well illustrated by Quantum Mechanics, where complex numbers are unquestionably the most appropriate choice to develop the theory. Pseudo-complex General Relativity evaluates the possibility that the gravitational interaction acquires its most natural description when constructed upon pseudo-complex numbers, which consist of one of the three possibilities of abelian complex numbers with a single imaginary unit. This numerical set is endowed with nonzero elements whose product is zero, such numbers are called generalized zeros or divisors of zero. The presence of generalized zeros allows the introduction of a modi ed variational principle from which an additional term, absent in General Relativity, emerges in the eld equations. This additional term is interpreted as a dark energy, whose physical origin is related to vacuum uctuations. The inclusion of this e ect is legitimate because a priori vacuum uctuations must gravitate as any other form of energy. From the eld equations we can summarize the main conceptual idea of the theory, in pseudo-complex General Relativity mass not only curves spacetime but also is able to change the structure of the spacetime around the mass. The di erences with respect to General Relativity are manifested in extreme physical situations in the regime of intense gravitational elds. As an application we analyze from the theoretical point of view an exotic compact object composed of fermionic dark matter.

O lado escuro do universo é misterioso e sua natureza é ainda desconhecida. De fato, isto talvez constitua o maior desafio da cosmologia moderna. As duas com- ponentes do setor escuro (mat´ eria escura e energia escura) correspondem hoje a cerca de noventa e cinco por cento do universo. O candidato mais simples para a energia energia é uma constante cosmológica. Contudo, esta tentativa apresenta uma enorme discrepância de 120 ordens de magnitude entre a predição teórica e os dados observados. Tal disparidade motiva os físicos a investigar modelos mais sofisticados. Isto pode ser feito tanto buscando um entendimento mais profundo de onde a constante cosmológica vem, se deseja-se derivá-la de primeiros princípios, quanto considerando outras possibilidades para a expansão acelerada, tais como modificações da relatividade geral, campos de matéria adi- cionais e assim por diante. Ainda considerando uma energia escura dinâmica, pode existir a possibilidade de interação entre energia e matéria escuras, uma vez que suas densidades são comparáveis e, dependendo do acoplamento usado, a interação pode também aliviar a questão de porquê as densidades de matéria e energia escura são da mesma ordem hoje. Modelos fenomenológicos tem sido amplamente estudados na literatura. Por outro lado, modelos de teoria de cam- pos que visam uma descrição consistente da interação energia escura/matéria escura ainda são poucos. Nesta tese, nós exploramos como candidato à energia escura um campo escalar ou vetorial em várias abordagens diferentes, levando em conta uma possível interação entre as duas componentes do setor escuro. A tese é dividida em três partes, que podem ser lidas independentemente. Na primeira parte, nós analisamos o comportamento asintótico de alguns modelos cosmológicos usando campos escalares ou vetorial como candidatos para a energia escura, à luz da teoria de sistemas dinâmicos. Na segunda parte, nós usamos um campo escalar em supergravidade para construir um modelo de energia escura dinâmico e também para incorporar um modelo de energia escura holográfica em supergravidade mínima. Finalmente, na terceira parte, nós propomos um modelo de energia escura metaestável, no qual a energia escura é um campo escalar com um potencial dado pela soma de auto-interações pares até ordem seis. Nós inserimos a energia escura metaestável em um modelo SU(2)R escuro, onde o dubleto de energia escura e o dubleto de matéria escura interagem nat- uramente. Tal interação abre uma nova janela para investigar o setor escuro do ponto-de-vista de física de partículas. Esta tese é baseada nos seguintes artigos, disponíveis também no arXiv: 1611.00428, 1605.03550, 1509.04980, 1508.07248, 1507.00902 e 1505.03243. O autor também colaborou nos trabalhos: 1607.03506 e 1605.05264. / The dark side of the universe is mysterious and its nature is still unknown. In fact, this poses perhaps as the biggest challenge in the modern cosmology. The two components of the dark sector (dark matter and dark energy) correspond today to around ninety five percent of the universe. The simplest dark energy candidate is a cosmological constant. However, this attempt presents a huge discrepancy of 120 orders of magnitude between the theoretical prediction and the observed data. Such a huge disparity motivates physicists to look into a more sophisticated models. This can be done either looking for a deeper understanding of where the cosmological constant comes from, if one wants to derive it from first principles, or considering other possibilities for accelerated expansion, such as modifications of general relativity, additional matter fields and so on. Still regarding a dynamical dark energy, there may exist a possibility of interaction between dark energy and dark matter, since their densities are comparable and, depending on the coupling used, the interaction can also alleviate the issue of why dark energy and matter densities are of the same order today. Phenomenological models have been widely explored in the literature. On the other hand, field theory models that aim a consistent description of the dark energy/dark matter interaction are still few. In this thesis, we explore either a scalar or a vector field as a dark energy candidate in several different approaches, taking into account a possible interaction between the two components of the dark sector. The thesis is divided in three parts, which can be read independently of each other. In the first part, we analyze the asymptotic behavior of some cosmological models using either scalar or vector fields as dark energy candidates, in the light of the dynamical system theory. In the second part, we use a scalar field in the supergravity framework to build a model of dynamical dark energy and also to embed a holographic dark energy model into minimal supergravity. Finally, in the third part, we propose a model of metastable dark energy, in which the dark energy is a scalar field with a potential given by the sum of even self-interactions up to order six. We insert the metastable dark energy into a dark SU(2)R model, where the dark energy doublet and the dark matter doublet naturally interact with each other. Such an interaction opens a new window to investigate the dark sector from the point-of-view of particle physics. This thesis is based on the following papers, available also in the arXiv: 1611.00428, 1605.03550, 1509.04980, 1508.07248, 1507.00902 and 1505.03243. The author also collaborated in the works 1607.03506 and 1605.05264.

Face à la nature inconnue de l'énergie noire et de la matière noire, des modèles à champ scalaire léger ont été proposés pour expliquer l'accélération tardive de l'expansion de l'Univers et l'apparente abondance de matière non baryonique dans l'Univers. Dans une première partie, cette thèse confronte de la façon la plus précise possible les données de cosmologie les plus récentes au modèle du Galiléon, une théorie de gravité modifiée possédant des propriétés théoriques particulièrement intéressantes. Des contraintes observationnelles sur les paramètres du modèle sont dérivées en utilisant les dernières mesures liées aux distances cosmologiques et à la croissance des grandes structures de l'Univers. Un bon accord est observé entre les données et les prédictions théoriques, faisant du Galiléon un modèle alternatif compétitif avec celui de la constante cosmologique. Dans une seconde partie, la production de Branons, particules scalaires candidates au statut de matière noire venant d'une théorie de dimensions supplémentaires, est recherchée dans les collisions proton-proton enregistrées en 2012 par l'expérience Compact Muon Solenoid auprès du Grand Collisionneur de Hadrons. Des événements présentant un photon et de l'énergie transverse manquante dans l'état final sont sélectionnés dans les données et comparés aux estimations des bruits de fonds attendus. Aucun excès d'événements n'étant observé, des limites expérimentales sur les paramètres de la théorie du Branon sont calculées. Elles sont les plus contraignantes à ce jour. Cette thèse se conclut par des arguments pour une description unifiée des deux modèles étudiés, dans le cadre des théories de dimensions supplémentaires. / The nature of dark energy and dark matter is still unknown today. Light scalar field models have been proposed to explain the late-time accelerated expansion of the Universe and the apparent abundance of non-baryonic matter. In the first part of this thesis, the Galileon theory, a well-posed modified gravity theory preserving the local gravitation thanks to the Vainshtein screening effect, is accurately tested against recent cosmological data. Observational constraints are derived on the model parameters using cosmological distance and growth rate of structure measurements. A good agreement is observed between data and theory predictions. The Galileon theory appears therefore as a promising alternative to the cosmological constant scenario. In the second part, the dark matter question is explored through an extra-dimension theory containing massive and stable scalar fields called Branons. Branon production is searched for in the proton-proton collisions that were collected by the Compact Muon Solenoid experiment in 2012 at the Large Hadron Collider. Events with a single photon and transverse missing energy are selected in this data set and compared to the Standard Model and instrumental background estimates. No signature of new physics is observed, so experimental limits on the Branon model parameters are derived. This thesis concludes with some ideas to reach an unified description of both models in the frame of extra-dimension theories.

<p>The propagation of light beams originating from synthetic ‘Type Ia’ supernovae, through an inhomogeneous universe with simplified dynamics, is simulated using a Monte-Carlo Ray-Tracing method. The accumulated statistical (redshift-magnitude) distribution for these synthetic supernovae observations, which is illustrated in the form of a Hubble diagram, produces a luminosity profile similar to the form predicted for a Dark-Energy dominated universe. Further, the amount of mimicked Dark-Energy is found to increase along with the variance in the matter distribution in the universe, converging at a value of Ω_X ≈ 0.7.</p><p>It can be thus postulated that at least under the assumption of simplified dynamics, it is possible to replicate the observed supernovae data in a universe with inhomogeneous matter distribution. This also implies that it is demonstrably not possible to make a direct correspondence between the observed luminosity and redshift with the distance of a cosmological source and the expansion rate of the universe, respectively, at a particular epoch in an inhomogeneous universe. Such a correspondences feigns an apparent variation in dynamics, which creates the illusion of Dark-Energy.</p>

The propagation of light beams originating from synthetic ‘Type Ia’ supernovae, through an inhomogeneous universe with simplified dynamics, is simulated using a Monte-Carlo Ray-Tracing method. The accumulated statistical (redshift-magnitude) distribution for these synthetic supernovae observations, which is illustrated in the form of a Hubble diagram, produces a luminosity profile similar to the form predicted for a Dark-Energy dominated universe. Further, the amount of mimicked Dark-Energy is found to increase along with the variance in the matter distribution in the universe, converging at a value of ΩX ≈ 0.7. It can be thus postulated that at least under the assumption of simplified dynamics, it is possible to replicate the observed supernovae data in a universe with inhomogeneous matter distribution. This also implies that it is demonstrably not possible to make a direct correspondence between the observed luminosity and redshift with the distance of a cosmological source and the expansion rate of the universe, respectively, at a particular epoch in an inhomogeneous universe. Such a correspondences feigns an apparent variation in dynamics, which creates the illusion of Dark-Energy.

The dark energy is one of the great mysteries of modern cosmology, responsible for the current acceleration of the expansion of our Universe. Its study is a major focus of my thesis : the way I choose to do so is based on the large-scale structure of the Universe, through a probe called the integrated Sachs-Wolfe effect (iSW). This effect is theoretically detectable in the cosmic microwave background (CMB) : before reaching us this light travelled through large structures underlain by gravitational potentials. The acceleration of the expansion stretches and flattens these potentials during the crossing of photons, changing their energy, in a way that depend on the properties of the dark energy. The iSW effect only has a weak effect on the CMB requiring the use of external data to be detectable. A conventional approach is to correlate the CMB with a tracer of the distribution of matter, and therefore the underlying potentials. This has been attempted numerous times with galaxies surveys but the measured correlation has yet to give a definitive result on the detection of the iSW effect. This is mainly due to the shortcomings of current surveys that are not deep enough and/or have a too low sky coverage. A part of my thesis is devoted to the correlation of FDC with another diffuse background, namely the cosmological infrared background (CIB), which is composed of the integrated emission of the non-resolved distant galaxies. I was able to show that it is an excellent tracer, free from the shortcomings of current surveys. The levels of significance for the expected correlation CIB-CMB exceed those of current surveys, and compete with those predicted for the future generation of very large surveys. In the following, my thesis was focused on the individual imprint in the CMB of the largest structures by iSW effect. My work on the subject first involved revisiting a past study of stacking CMB patches at structures location, using my own protocol, completed and associated with a variety of statistical tests to check the significance of these results. This point proved to be particularly difficult to assess and subject to possible selection bias. I extended the use of this detection method to other available catalogues of structures, more consequent and supposedly more sophisticated in their detection algorithms. The results from one of them suggests the presence of a signal at scales and amplitude consistent with the theory, but with moderate significance. The stacking results raise questions regarding the expected signal : this led me to work on a theoretical prediction of the iSW effect produced by structures, through simulations based on the Lemaître-Tolman-Bondi metric. This allowed me to predict the exact theoretical iSW effect of existing structures. The central amplitude of the measured signals is consistent with the theory, but shows features non-reproducible by my predictions. An extension to the additional catalogues will verify the significance of their signals and their compatibility with the theory. Another part of my thesis focuses on a distant time in the history of the Universe, called reionisation : the transition from a neutral universe to a fully ionised one under the action of the first stars and other ionising sources. This period has a significant influence on the CMB and its statistical properties, in particular the power spectrum of its polarisation fluctuations. In my case, I focused on the use of temperature measurements of the intergalactic medium during the reionisation in order to investigate the possible contribution of the disintegration and annihilation of the hypothetical dark matter. Starting from a theoretical work based on several models of dark matter, I computed and compared predictions to actual measures of the IGM temperature, which allowed me to extract new and interesting constraints on the critical parameters of the dark matter and crucial features of the reionisation itself