Type Ia supernovae (SNe Ia) are excellent tools in cosmology. Their intrinsic luminosities are found to vary systematically with the light-curve widths, providing an empirical calibration. This property, called the width-luminosity relation (WLR), is the basis of modern SN Ia cosmology and led to the unexpected discovery of the current accelerated rate of cosmic expansion. By examining the spectroscopic diversity of SNe Ia, this thesis aims to improve both the use of SNe Ia in cosmology and the physical understanding of the observed properties. Spectra of SNe Ia contain a wealth of information, but are difficult to organize. In this thesis, new methods are developed to consistently quantify and analyze the spectral features of supernovae. The efficacy of the methods is tested on a large library of observed spectra encompassing a wide range of properties. The spectroscopic diversity of SNe Ia enters cosmology through K-correction calculations. Before this work, K-correction was a major contributor of the systematic errors in cosmology. It is shown here that the systematic errors can be largely diminished by carefully quantifying the mean spectroscopic properties of SNe Ia. The remaining statistical errors are also quantified and shown to be redshift dependent. With the aid of principal component analysis (PCA), the multidimensional spectral information is reduced to a few components describing the largest variations in the spectral library. Using this tool, it is shown here that SN Ia intrinsic luminosity is the main driver of the spectroscopic diversity at maximum light, for every spectral feature from the ultraviolet to the near-infrared. These spectroscopic sequences can potentially account for a large fraction of the K-correction statistical errors and even enable the use of SN Ia spectra as independent indicators of intrinsic luminosity and colors. The established relations will also disentangle the effects of demographic shift and true evolution in high-redshift SN Ia spectra. The temporal evolution of the spectral features is shown to exhibit the persistence of the spectroscopic sequences throughout other epochs. The effect is attributed to the more rapid spectroscopic temporal evolution of fainter SNe Ia. This conclusion supports the theory that WLR is primarily a spectroscopic effect, rather than a bolometric one.

Η παρούσα μεταπτυχιακή διπλωματική εργασία πραγματεύεται την εισαγωγή ενός νέου πεδίου πεμπτουσίας, η ενέργεια του οποίου ταυτίζεται με το ενεργειακό απόθεμα της σκοτεινής ενέργειας του σύμπαντος. Η εισαγωγή ενός τέτοιου πεδίου αποτελεί εναλλακτική λύση στην προσπάθεια ερμηνείας της επιταχυνόμενης διαστολής του σύμπαντος που συνδέεται συνήθως με την κοσμολογική σταθερά Λ, των πεδιακών εξισώσεων Άινσταϊν. Παρότι έχουν προταθεί και άλλα μοντέλα πεδίων πεμπτουσίας, το συγκεκριμένο χαρακτηρίζεται από μία ιδιότητα που δεν επιτρέπει την εκτεταμένη παραβίαση της Αρχής της Ισοδυναμίας, που αποτελεί θεμελιώδη παραδοχή στην οποία στηρίζεται η Γενική Θεωρία της Σχετικότητας. Η μάζα των αντίστοιχων σωματιδίων εξαρτάται από την πυκνότητα ύλης σε κάθε περιοχή του σύμπαντος, εξ ου και το όνομα χαμαιλέοντες. Αφορμή για την εισαγωγή ενός τέτοιου πεδίου είναι η επιβεβαίωση της Αρχής της Ισοδυναμίας μέχρι κάποιο συγκεκριμένο όριο, πέραν του οποίου επιτρέπεται η εισαγωγή νέων μοντέλων αλληλεπιδράσεων που δεν έγιναν ακόμα αντιληπτές σε πληθώρα πειραμάτων. Όλα τα προηγούμενα αναφέρονται εν συντομία στο εισαγωγικό πρώτο κεφάλαιο. Στο δεύτερο κεφάλαιο γίνεται μια παρουσίαση της Αρχής της Ισοδυναμίας και του βαθμού παραβίασης της ο οποίος καθορίζει την ένταση της νέας θεμελιώδους δύναμης (fifth-force). Στο τρίτο κεφάλαιο, γίνεται μια ανασκόπηση του καθιερωμένου κοσμολογικού μοντέλου για το σύμπαν, που από παρατηρήσεις χαρακτηρίζεται από ομοιογένεια, ισοτροπία και σχεδόν επίπεδη γεωμετρία (WMAP-7). Με αυτά τα δεδομένα, καθώς και με τα πρόσφατα αποτελέσματα για ένα επιταχυνόμενα διαστελλόμενο σύμπαν προκύπτει η ανάγκη ύπαρξης ενός πεδίου με τα χαρακτηριστικά ενός σκοτεινού υγρού αρνητικής πίεσης και μάζας σε κοσμολογικές κλίμακες, της τάξης της σταθεράς Hubble στο παρόν (m_\phi\sim H_0\sim 10^{-33}eV). Η ανάγκη ύπαρξης ενός τέτοιου πεδίου (πάντα ως εναλλακτική της κοσμολογικής σταθεράς) παντού στο σύμπαν σε συνδυασμό με την μη ανίχνευση του μέχρι στιγμής σε κανένα πείραμα ή παρατήρηση, συνυπάρχουν στο μοντέλο των Khoury-Weltman για τα σωματίδια χαμαιλέοντες που εξετάζεται στο κεφάλαιο τέσσερα. Επειδή η μάζα του πεδίου εξαρτάται από την τοπική πυκνότητα ύλης, στη Γη η χαμαιλεοντική αλληλεπίδραση έχει πολύ μικρή εμβέλεια σε αντίθεση με την εμβέλεια σε κοσμολογικές κλίμακες και δεν γίνεται αντιληπτή. Επιπλέον η συνεισφορά στην αλληλεπίδραση σε ένα σώμα εκτός Γης από όλο τον όγκο της Γης είναι ελάχιστη και περιλαμβάνει μόνο αυτήν που προκαλείται από ένα λεπτό φλοιό στην επιφάνεια, όπου η τοπική πυκνότητα ύλης ελαττώνεται (thin-shell effect). Η νέα δύναμη το δυναμικό της οποίας είναι της μορφής Yukawa, θα είναι ασθενέστερη τουλάχιστον κατά τρεις τάξεις μεγέθους σε σύγκριση με τη βαρύτητας πειράματα στη Γη. Στο τελευταίο κεφάλαιο γίνεται μια παρουσίαση του CAST (Cern Solar Axion Telescope), στο οποίο θα μπορούσαν να ανιχνευτούν τα σωματίδια χαμαιλέοντες, λαμβάνοντας υπόψη την επέκταση του μοντέλου ώστε να περιλαμβάνει και ζεύξη με το ηλεκτρομαγνητικό πεδίο πέραν των πεδίων της ύλης. Οι χαμαιλέοντες που παράγονται από φωτόνια παρουσία ισχυρού μαγνητικού πεδίου στο θερμό πλάσμα του Ήλιου, φτάνουν στη Γη έχοντας ενέργεια της τάξης του 1keV και μπορούν να εισχωρήσουν στο εσωτερικό του μαγνήτη του CAST. Ο ισχυρός μαγνήτης του πειράματος που είναι ιδίου τύπου με αυτούς που απαρτίζουν τον Μεγάλο Αδρονικό Επιταχυντή (LHC), δημιουργεί μαγνητικό πεδίο της τάξης των 9Τ. Στο εσωτερικό του, οι χαμαιλέοντες θα μπορούσαν να επαναμετατραπούν σε φωτόνια και να ταυτοποιηθούν. Επιπλέον, ένα μικρό ποσοστό των χαμαιλεόντων που αφήνουν την επιφάνεια του Ήλιου μπορούν να μετατραπούν πίσω σε φωτόνια εξαιτίας των μαγνητικών πεδίων πάνω από τη φωτόσφαιρα. Αυτά τα φωτόνια θα έχουν φάσμα ενέργειας που κορυφώνεται στην περιοχή των μαλακών ακτίνων-Χ, οπότε θα δίνουν λύση στο πρόβλημα θέρμανσης του ηλιακού στέμματος (solar corona problem). / In the present Thesis, we review the chameleon field model and its discovery potential at CAST (Cern Axion Solar Telescope). The introduction of this new scalar field, of the so called quintessence type, is an alternative way of modeling the ubiquitous dark energy in the Universe, which drives its accelerated expansion. Moreover, the coupling of chameleons to photons enriches their discovery potential by experiments already operating such as CAST. Due to the fact that the mass of the field depends on the local matter density, in a dense environment such as the earth's surface the chameleon particle becomes heavy and undetectable. On the contrary, in cosmological scales the mass of the field is reduced to values related to the present Hubble's constant value (m_\phi\sim H_0\sim 10^{-33}eV) in order to coincide with the dark energy budget. This Thesis is organized in five chapters. The first chapter serves as a quick introduction to the subject of the current Thesis and the reasons for introducing a new field are stated. The second chapter refers to the Principle of Equivalence (E.P), a foundational principle of Einstein's General Relativity. It states that the gravitational mass of a freely falling body is proportional to its inertial mass. The level of verification of the former principle is of crucial importance for the characteristics of a quintessence field. If the E.P is not valid below a certain length scale, then the introduction of a quintessence field also implies the excistence of a new fundamental force in nature (fifth-force). In the third chapter, a small review of the standard cosmological model is made, which in combination with the results for an accelerated universe, leads to the necessity of introducing a new form of energy, dark energy. This form of energy behaves like a dark fluid of negative pressure (repulsive force) that tends to expand spacetime. It is modeled by adding the cosmological constant Λ, in Einstein's field equations or by introducing quintessence fields as the case of this Thesis. As already mentioned, the excistence of a quintessence field yields to violation of the Equivalence Principle. To overcome an extensive violation of the E.P the chameleon model is ``equipped'' by the peculiar property of its mass dependance on the environmental density. A second phenomenon related to the former property and the suppression of the E.P violation, is the ``Thin Shell Effect''. It simply states that the chameleonic profile of a large object is suppresed inside its bulk, and only a thin shell near its surface produces the chameleon force which is exerted on other massive bodies. This effect interprets the weakness and to date not discovered possible fifth-force. The fourth chapter ends up with a discussion on the fifth-force mediated by the chameleon particle. It is estimated that if such force exists, is about 3 orders-of-magnitude weaker than gravity. In the final chapter of this Thesis, the CAST experiment is presented. CAST has been operating for over ten years, searching for axions emitted by the Sun. It is believed that photons can oscillate to chameleons in the presence of a strong magnetic field in the Sun, travel through space and reach the Earth's surface where they can reconvert to photons inside the helioscope's pipe. The spectrum of the chameleons reaching the Earth is peaked at sub-keV region. Furthermore a small part of the chameleons leaving the Sun are converted back to photons over the photosphere due to the magnetic fields present there. These photons have energy lying in the soft X-ray region, hence addressing the solar corona problem.

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.

Made available in DSpace on 2016-12-12T20:15:48Z (GMT). No. of bitstreams: 1 INTRODUCAO.pdf: 361900 bytes, checksum: 61c5aed4cf4bc2e7a2cd004f090f00ab (MD5) Previous issue date: 2012-02-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work reviews concisely some of the theoretical attempts to explain the recently observed acceleration of the universe. Emphasis is put on the so-called theories f(R) which involve invariant modi.cations of the Einstein-Hilbert Lagrangian density. The pertinent .eld equations are derived from three distinct formalisms which are known in the literature as the metric formalism, the Palatini formalism and the a¢ ne formalism. For the case of the metric and Palatini formalisms, we carry out some interesting calculations and show the corresponding versions of the Friedmann equations. In addition, we present a minimally coupled Friedmann-Maxwell-f(R) model which may give a cosmological equation of state for w that agrees with available measurements of the red-shift of Ia supernovae. / Diante das observações experimentais da expansão cósmica acelerada, diversos - modelos teóricos surgiram para explicar a aceleração do Universo. Neste trabalho revisamos modelos tais como a constante cosmológica e quintessência, a qual é modelada por um campo escalar. O contexto aqui apresentado foi elaborado a partir das teorias modificadas da gravitação, também conhecidas como teorias f(R). Tal modelo é considerado uma generalização da ação de Einstein-Hilbert onde termos invariantes de curvatura podem descrever um regime acelerado para o universo. As equações de campo podem ser obtidas a partir de três formalismos distintos, a saber, formalismo métrico, Palatini e métrico-afim. Realizamos algumas manipulações algébricas para esses formalismos, bem como a apresentação das equações de Friedmann generalizadas para o formalismo métrico e Palatini. Também apresentamos um modelo no formalismo métrico com um campo de Maxwell acoplado minimamente. As equações de Friedmann-Maxwell-f(R), as quais dependem da forma funcional de f(R) como também do campo Fµv, permitem que uma equação de estado para w pode ser ajustada em concordância com as medidas do red-shift de supernovas IA.

Made available in DSpace on 2014-12-17T15:15:00Z (GMT). No. of bitstreams: 1 HeydsonHBS_TESE.pdf: 1323101 bytes, checksum: 18654a0afdabd08781b43fe6ac36fd9b (MD5) Previous issue date: 2014-04-16 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico / Significant observational effort has been directed to unveiling the nature of the so-called dark energy. However, given the large number of theoretical possibilities, it is possible that this a task cannot be based only on observational data. In this thesis we investigate the dark energy via a thermodynamics approach, i.e., we discuss some thermodynamic properties of this energy component assuming a general time-dependent equation-of-state (EoS) parameter w(a) = w0 + waf(a), where w0 and wa are constants and f(a) may assume different forms. We show that very restrictive bounds can be placed on the w0 - wa space when current observational data are combined with the thermodynamic constraints derived. Moreover, we include a non-zero chemical potential &#956; and a varying EoS parameter of the type &#969;(a) = &#969;0 + F(a), therefore more general, in this thermodynamical description. We derive generalized expressions for the entropy density and chemical potential, noting that the dark energy temperature T and &#956; evolve in the same way in the course of the cosmic expansion. The positiveness of entropy S is used to impose thermodynamic bounds on the EoS parameter &#969;(a). In particular, we find that a phantom-like behavior &#969;(a) < &#8722;1 is allowed only when the chemical potential is a negative quantity (&#956; < 0). Thermodynamically speaking, a complete treatment has been proposed, when we address the interaction between matter and energy dark / Esfor?os observacionais significativos t?m sido direcionados para investigar a natureza da chamada energia escura. No entanto, dado o grande n?mero de possibilidades te?ricas, esta tarefa n?o ? poss?vel baseando-se apenas em dados observacionais. Nesta tese, investigaremos a energia escura atrav?s da abordagem termodin?mica, isto ?, discutiremos algumas propriedades termodin?micas desta componente energ?tica assumindo um par?metro da equa??o de estado (EoS) geral dependente do tempo &#969;(a) = &#969;0 + &#969;af(a), onde &#969;0 e &#969;a s?o constantes e f(a) pode assumir diferentes formas. Mostraremos que limites muito restritivos podem ser colocados no espa?o &#969;0 &#8722; &#969;a quando dados observacionais recentes s?o combinados com os v?nculos termodin?micos derivados. Al?m disso, inclu?mos um potencial qu?mico &#956; n?o nulo e um par?metro da EoS vari?vel do tipo &#969;(a) = &#969;0 + F(a), portanto mais geral, nesta descri??o termodin?mica. Derivamos express?es gerais para a densidade de entropia e o potencial qu?mico, notando que a temperatura da energia escura T e &#956; evoluem da mesma maneira no decorrer da expans?o c?smica. A positividade da entropia S ? usada para impor limites termodin?micos ao par?metro da EoS &#969;(a). Em particular, encontramos que um comportamento tipo phantom &#969;(a) < &#8722;1 ? permitido somente quando o potencial qu?mico ? uma quantidade negativa (&#956; < 0). Termodinamicamente falando, um tratamento completo foi proposto, quando abordamos a intera??o entre mat?ria e energia escuras

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.

Le modèle cosmologique standard possède plusieurs lacunes pour une description pertinente de l’évolution de notre univers et de ses constituants. Tout d’abord, il laisse en suspens l’explication de l’origine de la matière noire et de l’énergie sombre. Ces composants, introduits ad hoc afin de satisfaire aux observations, représentent ensemble environ 95% du contenu en énergie de l’univers. Un second problème concerne l’indépendance d’échelle du modèle : quel que soit l’échelle du système considéré, il est attendu une dynamique et une géométrie identiques. Il est possible de se détourner du modèle standard et de s’intéresser à des cosmologies inhomogènes et à leur évolution moyenne. Selon ce formalisme, les inhomogénéités au sein d’une échelle influencent globalement la dynamique de cette dernière par un effet dit de rétroaction. Cette démarche très riche propose également une explication élégante au problème des constituants sombres : tous deux apparaissent comme une manifestation effective des inhomogénéités de distributions de matière et de géométrie. Cette thèse s’intéresse aux propriétés des modèles inhomogènes moyennés en relativité générale. Nous proposons dans un premier temps de décrire le comportement global des inhomogénéités selon une évolution de Chaplygin, et selon une évolution de Ginzburg-Landau. Nous montrons également l’instabilité gravitationnelle globale des solutions de Friedmann-Lemaître-Robertson-Walker. Cette classe de solutions est connue comme étant localement instable sous l’introduction de perturbations ; ici nous montrons qualitativement qu’elle ne fournit pas, en général, une approximation correcte en tant que fond physique. Nous présentons finalement une nouvelle théorie relativiste perturbative, pour laquelle les inhomogénéités scalaires évoluent autour d’un fond général, et non plus autour d’un fond de Friedmann-Lemaître-Robertson-Walker pré-défini. Cette nouvelle étude étend l’applicabilité des cosmologies inhomogènes, et pourrait éventuellement expliquer la formation des grandes structures sans recours à l’énergie noire / The standard cosmological model possesses some shortcomings for a relevent description of our universe and its constituents. First, it leaves in suspense the explanation of the origin of dark matter and dark energy. These components, introduced ad hoc in order to fit the observations, represent about 95% of the total energy. A second issue concerns the scale-independence of the model: whatever the scale of the considered system, it is expected identical dynamics and geometry. It is advisable to abandon the standard model and to focus on inhomogeneous cosmologies, and their average evolution. According to this formalism, inhomogeneities within a chosen scale globally impact on the dynamics of this latter through a so-called backreaction effect. This very rich approach also proposes an elegant explanation for the problem of the dark constituents: both stand for an effective manifestation of the inhomogeneities in the distributions of matter and geometry. This thesis focusses on the properties of averaged inhomogeneous models in general relativity. We first propose to describe the global behaviour of inhomogeneities according to a Chaplygin evolution, and according to a Ginzburg-Landau evolution. We also show the global gravitational instability of Friedmann-Lemaître-Robertson-Walker solutions. This class of solutions is already known to be locally gravitationaly unstable under the introduction of perturbations; here we show qualitatively that it does not furnish, in general, a good approximation as a physical background. We finally present a new relativistic perturbative scheme, in which scalar inhomogeneities evolve on a general background rather than on a pre-defined Friedmann-Lemaître-Robertson-Walker background. This new study extends the framework of application for inhomogeneous cosmologies, and may possibly explain the large-scale structure formation without the need for dark energy

Les missions modernes permettent d’accéder à des mesures de qualité pour les grandes structures, en échantillonnant la distribution de galaxies en détail jusque dans les régions les moins denses, les vides. Toutefois, nous observons les vides dans l’espace des redshift, ce qui limite notre connaissance de ces structures. Afin d’utiliser les vides en tant qu’outils cosmologiques de précision, il est fondamental d’obtenir leur forme dans l’espace réel. Dans cette thèse nous présentons un algorithme non-paramétrique permettant de reconstruire les profils de densité sphérique des vides empilés dans l’espace réel, sans assomption pour les distorsions en redshift. Nous obtenons donc les premiers profils de densité des vides empilés dans l’espace réel, à travers lesquels nous étudions la compensation de masse et calculons les profils de vitesses particulières des vides, se basant sur la théorie linéaire et le modèle cosmologique. Nous discutons l’utilisation des profils pour contraindre indépendamment les vitesses. Avec des catalogues simulés de galaxies, nous analysons l’effet des vitesses particulières sur les propriétés physiques des vides. Enfin nous calculons une prédiction du nombre de vides que fournira la future mission Euclid et des contraintes que ce nombre de vides donnera sur les paramètres cosmologiques (grâce au formalisme de Fisher). Les profils de densité de vides dans l’espace réel peuvent être utilisés pour tester les modèles cosmologiques (à travers l’étude de l’effet des vitesses particulières et l’amélioration du test de Alcock-Paczynski); l’étude des vides promet donc d’apporter des informations indépendantes pour éclaircir le mystère de l’énergie obscure. / Modern surveys allow us to access to high quality measurements, by sampling the galaxy distribution in detail also in the emptier regions, voids. When we observe cosmic voids, however, we observe them in redshift-space: their real shape remains inaccessible to us, thus limiting our knowledge about such structures. To employ voids as a precision tool for Cosmology, it is fundamental to obtain their real-space shape. This thesis presents a model-independent non-parametric algorithm to reconstruct the spherical density profiles of stacked voids in real space, without assumptions about redshift distortions. With this algorithm, we obtain the first ever real-space density profiles of stacked voids. With the profiles we study the mass compensation and obtain a theoretical prediction for the velocity profiles of voids based on linear theory and assuming cosmological parameters. In parallel, we discuss the use of the real-space profiles to obtain model-independent information about the peculiar velocity profiles of voids. Also, using mock catalogues, we analyse the effect of peculiar velocities on void properties and discuss it in the framework of current and future surveys. Finally we calculate a forecast for void abundances with the future Euclid mission and obtain, using the Fisher matrix formalism, a prediction for the constraints that void abundances will set on cosmological parameters. The real-space profiles of voids can be used to test cosmological models (through the understanding of peculiar velocities effects and the improvement of the Alcock-Paczynski test); and void abundances promise to bring independent information and to shed light on the mystery of dark energy.

Temnáenergietvořícípřibližně70%hmotyvesmíruz·stávájednouznejvětšch záhad moderní fyziky. K pochopení její podstaty jsou potřeba přesná kosmolog- ická měření. Jedním z projekt· zkoumající tuto exotickou formu hmoty bude i Large Synoptic Survey Telescope, který pom·že potvrdit či vyvrátit standardní kosmologický model (ΛCDM). Pro úspěch projektu je potřeba prozkoumat r·zné teorie temné energie. Jednou z alternativních teoríí vysvětlujících urychlenou expanzi vesmíru je tzv. chameleoní gravitace. Chameleon je nové skalární pole s hmotou závisející na okolní hustotě. V hustých prostředích jako je například Sluneční soustava získává pole velkou hmotu a propaguje se pouze na malých vzdálenostech díky čemuž m·že uniknout standardním test·m gravitace. V prá- ci mimo jiné studujeme chování chameleoního pole v okolí hvězd a v galaxiích. Ukazujeme také za jakých okolností je toto pole možné detekovat pomocí spek- troskopických měření a slabého čočkování.