<p>This thesis presents a brief review of gravitation and cosmology, and then gives an overview of the theory of cosmological perturbations; subsequently some applications are discussed, such as large-scale structure formation. Cosmological perturbations are here presented both in the Newtonian paradigm and in two di¤erent relativistic approaches. The relativistic approaches are (i) the metric approach, where small variations of the metric tensor are considered, and (ii) the covariant approach, which focusses on small variations of the curvature. Dealing with these two approaches also involves addressing the gauge problem –how to map an idealized world model into a more accurate world model.</p>

<p>Type Ia supernovae can be used as distance indicators for probing the expansion history of the Universe. The method has proved to be an efficient tool in cosmology and played a decisive role in the discovery of a yet unknown energy form, dark energy, that drives the accelerated expansion of the Universe. The work in this thesis addresses the nature of dark energy, both by presenting existing data, and by predicting opportunities and difficulties related to possible future data.</p><p>Optical and infrared measurements of type Ia supernovae for different epochs in the cosmic expansion history are presented along with a discussion of the systematic errors. The data have been obtained with several instruments, and an optimal method for measuring the lightcurve of a background contaminated source has been used. The procedure was also tested by applying it on simulated images.</p><p>The future of supernova cosmology, and the target precision of cosmological parameters for the proposed SNAP satellite are discussed. In particular, the limits that can be set on various dark energy scenarios are investigated. The possibility of distinguishing between different inverse power-law quintessence models is also studied. The predictions are based on calculations made with the Supernova Observation Calculator, a software package, introduced in the thesis, for simulating the light propagation from distant objects. This tool has also been used for investigating how SNAP observations could be biased by gravitational lensing, and to what extent this would affect cosmology fitting. An alternative approach for estimating cosmological parameters, where lensing effects are taken into account, is also suggested. Finally, it is investigated to what extent strongly lensed core-collapse supernovae could be used as an alternative approach for determining cosmological parameters.</p>

We use recently published redshift space distortion measurements of the cosmological growth rate, f sigma(8)(z), to examine whether the linear evolution of perturbations in the R-h = ct cosmology is consistent with the observed development of large-scale structure. We find that these observations favour R-h = ct over the version of Lambda cold dark matter (Lambda CDM) optimized with the joint analysis of Planck and linear growth rate data, particularly in the redshift range 0 < z < 1, where a significant curvature in the functional form of f sigma(8)(z) predicted by the standard model-but not by R-h = ct-is absent in the data. When Lambda CDM is optimized using solely the growth rate measurements; however, the two models fit the observations equally well though, in this case, the low-redshift measurements find a lower value for the fluctuation amplitude than is expected in Planck Lambda CDM. Our results strongly affirm the need for more precise measurements of f sigma(8)(z) at all redshifts, but especially at z < 1.

Many measurements in cosmology depend on the use of integrated distances or time, but. galaxies evolving passively on a timescale much longer than their age difference allow us to determine the expansion rate H(z) solely as a function of the redshift-time derivative dz/dt. These model-independent "cosmic chronometers" can therefore be powerful discriminators for testing different cosmologies. In previous applications, the available sources strongly disfavored models (such as Lambda CDM) predicting a variable acceleration, preferring instead a steady expansion rate over the redshift range 0 less than or similar to z less than or similar to 2. A more recent catalog of 30 objects appears to suggest non-steady expansion. In this paper, we show that such a result is entirely due to the inclusion of a high, locally inferred value of the Hubble constant H-0 as an additional datum in a set of otherwise pure cosmic-chronometer measurements. This H-0, however, is not the same as the background Hubble constant if the local expansion rate is influenced by a Hubble Bubble. Used on their own, the cosmic chronometers completely reverse this conclusion, favoring instead a constant expansion rate out to z similar to 2.

We continue to build support for the proposal to use H II galaxies (HIIGx) and giant extragalactic H II regions (GEHR) as standard candles to construct the Hubble diagram at redshifts beyond the current reach of Type Ia supernovae. Using a sample of 25 high-redshift HIIGx, 107 local HIIGx, and 24 GEHR, we confirm that the correlation between the emission -line luminosity and ionized -gas velocity dispersion is a viable luminosity indicator, and use it to test and compare the standard model Lambda CDM and the R-h = ct universe by optimizing the parameters in each cosmology using a maximization of the likelihood function. For the flat Lambda CDM model, the best fit is obtained with Omega(m) = 0.40(-0.09)(+0.09). However, statistical tools, such as the Akaike (AIC), Kullback (KIC) and Bayes (BIC) Information Criteria favour R-h = Ct over the standard model with a likelihood of approximate to 94.8-98.8 per cent versus only per cent. For wCDM (the version of ACDM with a dark -energy equation of state wde = Pde/Pde rather than was t WA = 1), a statistically acceptable fit is realized with Omega(m) = 0.221(-0.14)(+0.16) and wde = 0.511'0'21-5" which, however, are not fully consistent with their concordance values. In this case, wCDM has two more free parameters than R-h = Ct, and is penalized more heavily by these criteria. We find that R-h = Ct is strongly favoured over wCDM with a likelihood of approximate to 92.9-99.6 per cent versus only 0.4-7.1 per cent. The current HIIGx sample is already large enough for the BIC to rule out ACDM/wCDM in favour of R-h = Ct at a confidence level approaching 3 sigma.

The so-called 'cosmic web', comprising cosmic voids and galaxy clusters, has been proven to be extremely sensitive to deviations from General Relativity. This could be further investigated by future large-scale surveys, such as with the European Space Agency satellite Euclid. In this study, the parameter |fR0| from f(R) gravity is constrained by considering the Euclid survey specications to predict the observed numbers of voids and clusters in bins of redshift, mass and, only for voids, density contrast. From these values, the Fisher matrix is computed for three values of |fR0|, 10-4, 10-6 and 10-8, by assuming a flat Universe with a component that mimics the cosmological constant. The probability density functions are obtained for |fR0| and seven other parameters from the fiducial model considered (ns, h, Ωb, Ωm, σ8, w0 and wa).

Nesta dissertação, uma revisão dos modelos cosmológicos newtonianos e neo-newtonianos baseados na formulação da hidrodinâmica clássica é apresentada, com especial ênfase para os resultados básicos e as limitações mais importantes dessas abordagens. Em seguida, mostramos que a descrição Lagrangiana clássica proposta por Lima, Moreira e Santos (1998) para fluidos simples, pode ser generalizada para incluir modelos com misturas de fluidos, e portanto, cosmologias mais realísticas contendo bárions, matéria escura e energia escura, bem como qualquer forma de interação entre essas componentes. Neste trabalho propomos uma descrição lagrangiana clássica para modelos relativísticos do tipo FRW. Nesta descrição, o comportamento dinâmico do fator de escala a(t), como previsto pelas cosmologias relativísticas, é substituído pelo movimento unidimensional de uma partícula teste de massa m sob a ação de um potencial clássico, V(x), onde x é a coordenada unidimensional da partícula. O tratamento pode ser aplicado para os mais diversos cenários de energia escura. Para exemplificar, discutimos com detalhe os seguintes modelos contendo matéria escura e energia escura: XCDM, X(z)CDM, Lambda CDM, Lambda(t) e gás de Chaplygin. Por completeza, modelos multidimensionais do tipo FRW também são considerados. Em todos esses modelos, o parâmetro de curvatura k das seções espaciais das cosmologias determina a energia total da partícula teste pela relação, E=-mk/2, tal como ocorre nos modelos de fluidos simples. As propriedades dinâmicas associadas com o presente estágio de aceleração do universo são univocamente descritas em termos da função potencial do sistema. Finalmente, utilizando os dados da distância de luminosidade provenientes das supernovas do tipo Ia, discutimos como o potencial unidimensional pode ser reconstruído a partir das observações. / In this dissertation, a review of the Newtonian and neo-Newtonian cosmological models based on the classical hydrodynamics formulation is presented with special emphasis to the basic results and the main limitations of such approaches. Next, we show that the classical Lagrangian description as proposed by Lima, Moreira & Santos (1998) for simple fluids, can be generalized to include fluid mixtures, and, therefore, more realistic cosmologies containing baryons, dark matter and dark energy, as well as, any kind of interaction among such components. In the lagrangian description, the dynamic behavior of the scale factor a(t), as predicted by the relativistic cosmologies, is replaced by the unidimensional motion of a test particle with mass m under the action of a classical potential, V(x), where x(t) is the coordinate of the particle. The treatment can be applied for many different scenarios of dark energy. In order to exemplify, we discuss with detail the following models containing dark matter and dark energy: XCDM, X(z)CDM, Lambda(t)CDM and the Chaplygin gas. For completeness, FRW type multidimensional models are also considered. For all these models, the curvature parameter k of the spatial sections in the relativistic cosmologies determines the total energy by the relation, E=-mk/2, as occurs in the simple fluid models. The dynamic property associated with the present accelerating stage of the Universe are univocally described in terms of the potential function of the system. Finally, by using the data from luminosity distance of supernovae type Ia, we discuss how the unidimensional potential can be reconstructed from the observations.

Ce travail prend pour point de départ Leçons sur les hypothèses cosmogoniques de Henri Poincaré, ouvrage qui est issu de son cours à la Sorbonne et l'une de ses dernières publications. L'objectif du travail est de restituer la pensée cosmologique du mathématicien et de l'inscrire dans l'histoire de la cosmologie, proposant une introduction aux Leçons et une grille de lectures historiques et philosophiques de cet ouvrage autour de deux axes : la cosmologie classique et la philosophie poincaréenne. La première partie est consacrée à la science classique qui oscille entre la possibilité d'une cosmogonie mécaniste et l'impossibilité d'une cosmologie en tant que science. L'ambivalence s'observe chez les auteurs des XVIIe et XVIIIe siècles notamment Kant et Laplace avec leur hypothèse cosmogonique, jusqu'au XIXe siècle qui reste récitent à s'étendre au-delà du système solaire et développer une cosmologie proprement dite. La seconde partie de la thèse vise une lecture systématique de l'œuvre de Poincaré à partir des trois ouvrages philosophiques composés et édités par lui-même comme La science et l'hypothèse. La lecture procède en trois temps, autour de trois problèmes : 1° la stabilité et le mécanisme, mis en question par la thermodynamique et le probabilisme (avant 1900) ; 2° la loi et le principe en mécanique et en physique, notamment le principe de relativité et le second principe de la thermodynamique, mis en question par le développement de la physique (1900-1905) ; 3° l'espace, mis en lumière par la nouvelle mécanique et la théorie cinétique (après 1905). Chaque problème est ouvert ou dirigé vers la problématique cosmologique, sans pour autant qu'elle soit poursuivie dans le concret ni dépasser le niveau conceptuel. Ainsi Poincaré est amené aux hypothèses cosmogoniques, pour finir par une philosophie plutôt qu'une cosmologie. / This study takes as a primary source Lectures on Cosmogonic Hypotheses of Henri Poincaré, which was originally his course at the Sorbonne and one of his last publications. With the main objective to understand the cosmological thinking of Poincaré and its place in the history of cosmology, I propose an introduction to Lectures and its historical and philosophical reading around two axes: classical cosmology and Poincaré's philosophy. The first part is devoted to Classical Science to show how it seeks both the possibility of a mechanistic cosmogony and the impossibility of a cosmology as a science. This ambivalence can be seen in authors of the 17th and 18th centuries, especially Kant and Laplace with their cosmogonic hypothesis, as well as in the 19th century, when cosmological thinking remained speculative and restricted to the solar system, despite the advance of astronomy and physics, both in theory and observation. The second part suggests a systematic reading of Poincaré's philosophy from three philosophical books composed and edited by himself such as Science and Hypothesis. The reading proceeds in three steps, divided by a chronological order which is also thematic and problematic: (1) stability and mechanism, questioned by thermodynamics and probability theory (before 1900); (2) law and principle of mechanics and physics, especially the principle of relativity and the second principle of thermodynamics (1900-1905); 3 ° space, in the light of the new mechanics and the kinetic theory of gases (after 1905). Each problem shows its own cosmological moment that remains at the conceptual rather than the concrete level. Thus Poincaré is led to cosmogonic hypotheses, ending with a philosophy rather than a cosmology.

Type Ia supernovae can be used as distance indicators for probing the expansion history of the Universe. The method has proved to be an efficient tool in cosmology and played a decisive role in the discovery of a yet unknown energy form, dark energy, that drives the accelerated expansion of the Universe. The work in this thesis addresses the nature of dark energy, both by presenting existing data, and by predicting opportunities and difficulties related to possible future data. Optical and infrared measurements of type Ia supernovae for different epochs in the cosmic expansion history are presented along with a discussion of the systematic errors. The data have been obtained with several instruments, and an optimal method for measuring the lightcurve of a background contaminated source has been used. The procedure was also tested by applying it on simulated images. The future of supernova cosmology, and the target precision of cosmological parameters for the proposed SNAP satellite are discussed. In particular, the limits that can be set on various dark energy scenarios are investigated. The possibility of distinguishing between different inverse power-law quintessence models is also studied. The predictions are based on calculations made with the Supernova Observation Calculator, a software package, introduced in the thesis, for simulating the light propagation from distant objects. This tool has also been used for investigating how SNAP observations could be biased by gravitational lensing, and to what extent this would affect cosmology fitting. An alternative approach for estimating cosmological parameters, where lensing effects are taken into account, is also suggested. Finally, it is investigated to what extent strongly lensed core-collapse supernovae could be used as an alternative approach for determining cosmological parameters.

This thesis presents a brief review of gravitation and cosmology, and then gives an overview of the theory of cosmological perturbations; subsequently some applications are discussed, such as large-scale structure formation. Cosmological perturbations are here presented both in the Newtonian paradigm and in two di¤erent relativistic approaches. The relativistic approaches are (i) the metric approach, where small variations of the metric tensor are considered, and (ii) the covariant approach, which focusses on small variations of the curvature. Dealing with these two approaches also involves addressing the gauge problem –how to map an idealized world model into a more accurate world model.