Recent research in science indicates that we are living in a fine-tuned universe. Only a very small parameter space of universal fundamental constants in Physics is congenial for the existence of life. Moreover, recent studies in Biological evolution also reveal that fine-tuning did exist in the evolution. It seems that we are so lucky to exist as all universal fundamental constants and life-permitting factors really fall into such a very small life-allowing region. This problem is known as the fine-tuning problem. Does this phenomenon need an explanation? Can the fine-tuning problem point to the existence of God? Modern Science invokes the idea of multiverse to address the fine-tuning problem. Some scientists suggest that each universe in a set of infinitely many universes contains a typical set of fundamental constants. We should not be surprised why our universe is fine-tuned because we would not exist if the constants are not the life-allowed values. Some suggest that the existence of God can explain this fine-tuning problem. The naturalistic multiverse theory and the existence of God are the two most robust proposals to address the fine-tuning problem. Moreover, some argue that the fine-tuning problem is not real because we are just subject to observational selection effect. In this thesis, I will provide a comprehensive discussion on the fine-tuning phenomena in our universe. In particular, I will use the confirmation principle and the inference to the best explanation simultaneously to evaluate different hypotheses in a more systematic way and give some of the new and updated scientific and philosophical arguments to respond to the recent criticisms of the fine-tuning arguments. I conclude that the theistic hypothesis is the best among all to address the fine-tuning problem.

Some implications and consequences of the expansion of the universe are examined. In Chapter 1 it is shown that this expansion creates grave difficulties for the Hoyle-Narlikar theory of gravitation. Chapter 2 deals with perturbations of an expanding homogeneous and isotropic universe. The conclusion is reached that galaxies cannot be formed as a result of the growth of perturbations that were initially small. The propagation and absorption of gravitational radiation is also investigated in this approximation. In Chapter 3 gravitational radiation in an expanding universe is examined by a method of asymptotic expansions. The 'peeling off' behaviour and the asymptotic group are derived. Chapter 4 deals with the occurrence of singularities in cosmological models. It is shown that a singularity is inevitable provided that certain very general conditions are satisfied.

This thesis consists of two main parts, both of which focus on Bayesian methods and the problem of model selection in particular. The first part investigates a new approach to computing the Bayes factor for model selection without needing to compute the Bayesian evidence, while the second part shows, through an analytical calculation of the Bayesian evidence, that Bayesian methods allow two point sources to be distinguished from a single point source at angular separations that are much smaller than the naive beam size at high signal to noise. In the first part, the idea is to create a supermodel by combining two models using a hyperparameter, which we call α. Setting α = 0 or 1 switches each of the models off. Hence, the ratio of the posterior of α at the two end points (0 or 1) gives the Bayes Factor. This effectively converts the problem of model selection into a Bayesian inference problem. One can then use a standard Markov Chain Monte Carlo method to map the posterior distribution of α and compute the Bayes factor. In the second part of this thesis, the Bayesian radio interferometry formalism of Lochner et al. (2015) is extended to take into account the gains of the antennae using the StEFCal algorithm, an important part of the calibration pipeline. Finally we study the case of a pair of sources and show that they can be resolved using an analytical computation of the Bayesian evidence. This demonstrates that Bayesian methods allow super-resolution: the pair of sources can be distinguished from a single source at arbitrarily small scales compared to the naive beam size, as long as the measurements have sufficient signal to noise.

Here we initiate a systematic study of some of the symmetry properties of unimodular gravity, building on much of the known structure of general relativity, and utilizing the powerful technology developed in that context, such as the spinor helicity formal-ism. In particular, we show, up to five-points and tree-level, that the KLT relations of perturbative gravity hold for trace free or unimodular gravity. This work is in conjunction with a paper written with A. Welman, J. Murugan and G.F.R. Ellis (ARXIV: 1511.08517)

Bibliography: pages 107-113. / A review of standard cosmology theory and observational results is presented. The main tool for investigating large-scale structure in this thesis is a visually compiled void catalogue. Void selection effects that cause the detected distribution of voids to differ from the true distribution are discussed and suggestions are made for how to correct for these effects in the catalogue. The geometrical distribution of voids is then studied by dividing the void catalogue into two parts - wall voids and non-wall voids. The wall voids are smaller with typical radii of around 150 km s-¹ whereas non-wall voids have a mean radius of approximately 1150 km s-¹. The non-wall, and therefore, the larger voids are distributed isotropically and their correlation function is found to correspond roughly to that of Abell clusters, thus suggesting a link between the two structures. A relation between the velocity dispersions of clusters and the void radii is found using a spherical collapse model for structure formation. The ratio of these two quantities is used to put constraints on the cosmic density parameter 0 and observational data indicate that the universe is open.

The basic theory of observations of galaxies in a cosmological context is reviewed and extended to include e.g. the pointspread effect of the atmosphere. From this the relation between the sources (objects) and the images of these sources is derived (the observational map). A program is developed to calculate this map and some results are given.

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Orientador: Horatiu Nastase / Resumo: Nesta tese, discutimos três modelos cosmológicos que são baseados direta ou indiretamente em ideias advindas de teoria das cordas. Depois de uma revisão geral de cosmologia em teoria das cordas, um resumo de cosmologia e teoria das cordas é apresentado, com ênfase nos conceitos fundamentais e teóricos. Então descrevemos como o acoplamento camaleônico pode potencialmente afetar as predições de inflação cósmica com campo único, com tratamento cuidadoso dos modos de perturbação cosmológica adiabáticos e de entropia. Além disso uma nova abordagem para a dualidade-T em soluções cosmológicas de supergravidade bosônica é discutida no contexto de teoria dupla de campos. Por fim, propomos uma nova prescrição para o mapa holográfico em cosmologia que pode ser usado para conectar modelos fundamentais de cosmologia holográfica com outras abordagens fenomenológicas. / Doutor

<p>It is an intriguing possibility that our world may consist of more than three spatial dimensions, compactified on such a small scale that they so far have escaped detection. In this thesis, a particular realization of this idea -- the scenario of so-called 'universal extra dimensions' (UED) -- is studied in some detail, with a focus on cosmological consequences and appplications.</p><p>The first part investigates whether the size of homogeneous extra dimensions can be stabilized on cosmological time scales. This is necessary in order not to violate the stringent observational bounds on a possible variation of the fundamental constants of nature.</p><p>An important aspect of the UED model is that it can provide a natural explanation for the mysterious dark matter, which contributes nearly thirty times as much as luminous matter like stars, galaxies etc. to the total energy content of the universe. In the second part of this thesis, the observational prospects for such a dark matter candidate are examined. In particular, it is shown how dark matter annihilations taking place in the Milky Way could give rise to exotic contributions to the cosmic ray spectrum in photons and antiprotons, leading to distinct experimental signatures to look for.</p><p>This includes a comparison with similar effects from other dark matter candidates, most notably the neutralino, which appears in supersymmetric extensions of the standard model of particle physics.</p>

It is an intriguing possibility that our world may consist of more than three spatial dimensions, compactified on such a small scale that they so far have escaped detection. In this thesis, a particular realization of this idea -- the scenario of so-called 'universal extra dimensions' (UED) -- is studied in some detail, with a focus on cosmological consequences and appplications. The first part investigates whether the size of homogeneous extra dimensions can be stabilized on cosmological time scales. This is necessary in order not to violate the stringent observational bounds on a possible variation of the fundamental constants of nature. An important aspect of the UED model is that it can provide a natural explanation for the mysterious dark matter, which contributes nearly thirty times as much as luminous matter like stars, galaxies etc. to the total energy content of the universe. In the second part of this thesis, the observational prospects for such a dark matter candidate are examined. In particular, it is shown how dark matter annihilations taking place in the Milky Way could give rise to exotic contributions to the cosmic ray spectrum in photons and antiprotons, leading to distinct experimental signatures to look for. This includes a comparison with similar effects from other dark matter candidates, most notably the neutralino, which appears in supersymmetric extensions of the standard model of particle physics.