Submitted by Emanuel Varela Cardoso (emanuel.varela@ufcg.edu.br) on 2018-10-18T17:24:51Z No. of bitstreams: 1 LEONARDO RIBEIRO COLAÇO – DISSERTAÇÃO (PPGFísica) 2016.pdf: 3372949 bytes, checksum: 8387f15d435a4dd929618ecca701927e (MD5) / Made available in DSpace on 2018-10-18T17:24:51Z (GMT). No. of bitstreams: 1 LEONARDO RIBEIRO COLAÇO – DISSERTAÇÃO (PPGFísica) 2016.pdf: 3372949 bytes, checksum: 8387f15d435a4dd929618ecca701927e (MD5) Previous issue date: 2018 / Capes / As teorias cosmológicas mais comumente aceitas são baseadas no pressuposto de que as constantes fundamentais da natureza, como a constante gravitacional G, a constante de estrutura fina α, entre outras, são de fato constantes. Sendo assim, a suposição de que essas constantes não variam no espaço-tempo é apenas uma hipótese, precisando então ser comprovada a partir de dados experimentais. Neste trabalho, propomos um novo método, independente de modelo cosmológico, capaz de investigar uma possível variação como redshift da constante de estrutura fina, α=е2 /hc, onde é a carga elementar, h é a constante de Planck dividida por 2 π e c é a velocidade da luz. Para tal fim, mostramos também que a técnica combinada do Efeito Sunyaev-Zel'dovich (ESZ) como Brilho Superficial em raios-X (SX) para se medir Distância de Diâmetro Angular (DDA) dos Aglomerados de Galáxias (AG) é dependente da constante de estrutura fina. Mais precisamente,se = 0 (z), argumentamos que os dados atuais dessa técnica fornecem DobsA (z) = 2(z)DA(z), onde DA(z) é a verdadeira DDA para o aglomerado de galáxias e (z) é o campo escalar Dilaton que governa uma possível variação em α. Considerando uma amostra de 25 medidas de DobsA (z), feitas por De Filippis et al. (2005),via ESZ/SX na faixa de redshift 0; 023 < zAG < 0; 784 e estimando medidas de DA(z) do assim chamado Union 2.1 Compilation de Super nova e tipoIa (SNeIa), onde o redshift das SNeIa foram cuidadosamente selecionados para coincidir como redshift do aglomerado de galáxias associado com a maior diferença de redshift obedece a jzAG 􀀀 zSNej < 0; 005. Portanto, foi possível atribuir algumas restrições sobre uma possível variação de α para uma classe de Modelos Dilaton Run away, (z) =1􀀀 ln (1+ z). Nossas análises mostraram que = 􀀀0; 037 0; 157 em 1 , ou seja, nossas análises são compatíveis com uma não variação da constante de estrutura fina. / The most common accepted cosmological theories are base don the assumption that the fundamental constants of nature, suchas the gravitational constant G, the new structure constant α, and others, are infact constant. Thus, the assumption that these constants do not vary with time or space is only a hypothesis, then it needs to be confirmed from experimental data. In this paper, we propose a new method, independent of cosmological models, which is cap able to investigate a possible variation with redshift of the new structure constant, α = e2=hc, where e is the elementary charge, h is Planck's constant over 2π and c is the speed of light. For that purpose, we also show that the combined technique between Sunyaev-Zel'doviche effect (SZE) and X-ray surface brightness (SX) to measure Angular Diameter Distance (ADD) of Galaxy Clusters (GC), dependents on the new structure constant. More precisely, if α = α0 (z) we argue that the current data of this technique gives DobsA (z) = 2(z)DA(z), where DA(z) is the true ADD for galaxy clustersand (z) is the dilatons calareld that governs a possible variation of α. We considere da sample of 25 measurements of Dobs A (z), made by De Filipp is e tal. (2005),via ESZ/SX in the range of redshift 0:023 < zGC < 0:784 and we also estimated DA(z) from the so-called Union 2.1 Super novaeIa(SNEIa) Compilation,where the SNeIa redshifts were carefully selected to match the one soft he as sociated galaxy cluster with the larger redshiftd iαe rencefollows jzGC 􀀀� zSNej < 0:005. There for e,it was possible to put some constraints on a possible variation of α for a class of Dilaton Run a way Model, (z) =1 􀀀� ln (1+ z). We obtained = 􀀀�0; 037 0; 157 in1 , i.e.,our analysis is compatible with an on variation of the new structure constant.

This thesis contributes to the field of dark energy and observational cosmology. We have investigated possible direction dependent systematic signal and non-Gaussian features in the supernovae (SNe) Type Ia data. To detect these effects we propose a new method of analysis. Although We have used this technique on SNe Ia data, it is quite general and can be applied to other data sets as well. SNe Ia are the most precise known distance indicators at the cosmological distances. Their constant peak luminosity(after correction) makesthem standard candles and hence one can measure the distances in the universe using SNe Ia. This distance measurement can determine various cosmological parameters such as the Hubble constant, various components of matter density and dark energy from, the SNe Ia observations. Recent SNe Ia observations have shown that the expansion of the universe is currently accelerating. This recent acceleration is explained by invoking a component in the universe having negative pressure and is termed as dark energy. It can be described by a homogeneous and isotropic fluid with the equation of state P = wρ, where w is allowed to be negative. A constant(Λ) in the Einstein equation(known as cosmological constant) can explain the acceleration, in the fluid model it can be modeled with w = -1. Other models of dark energy with w = -1 can also explain the acceleration, however the precise nature of this mysterious component remains unknown. Although there exist a wide range of dark energy models, cosmological constant provides the simplest explanation to the acceleration of the expansion of the Universe. The equation of state parameter w has been investigated by recent surveys but the results are still consistent with a wide range of dark energy models. In order to discriminate among various cosmological models we need an even more precise measurement of distance and error bars in the SNe Ia data. From the central limit theorem we expect Gaussian errors in any experiment that is free from systematic noise. However in astronomy we do not have a control over the observed phenomena and thus can not control the systematic errors (due to some physical processes in the Universe) in the observed data. The only possible way to deal with such data is by using appropriate statistical techniques. Among these systematic features the direction dependent features are more dangerous ones since they may indicate a preferred direction in the Universe. To address the issue of direction dependent features we have developed a new technique(Δ statistic henceforth) which is based on the extreme value theory. We have applied this technique to the available high-z SNe Ia data from Riess et al.(2004)and Riess et al.(2007). In addition we have applied it to the HST data from HST key project for H0 measurement. Below we summarize the material presented in the thesis. Chapter wise summary of the thesis In the first chapter we present an introductory discussion of the various basic cosmological notions eg. Cosmological Principle (CP), observational evidence in support of CP and departures from it, distance measures and large scale structure. The observed departures from the CP could be present due to the systematic errors and/or non-Gaussian error bars in the data. We discuss the errors involved in the measurement process Basics of statistical techniques : In the next two chapters we discuss basics of the statistical techniques used in this thesis and extreme value theory. Extreme value theory describes how to calculate the distribution of extreme events. The simplest of the distributions of the extremes is known as the Gumbel distribution. We discuss features of the Gumbel distribution since it is used extensively in our analysis. Δ statistic and features in the SNe data : In the fourth chapter we derive Δ statistic and apply it to the SNe Ia data sets. An outline of the Δ statistic is as follows : a) We define a plane which cuts the sky into hemispheres. This plane will divide the data into two subsets, one in each hemisphere. b) Now we calculate the χ2 in each hemisphere for an FRW universe assuming a flat geometry. c) The difference of χ2 in the two hemisphere is calculated and maximized by rotating the plane. This maximum should follow the Gumbel distribution. Since it is difficult to calculate the analytic form of Gumbel distribution we calculate it numerically assuming Gaussian error bars. This gives the theoretical distribution for the above calculated maximum of difference of χ2 . The results indicate that GD04 shows systematic effects as well non-Gaussian features while the set GD07 is better in terms of systematic effects and non-Gaussian features. Non-Gaussian features in the H0 data : HST key project measures the value of Hubble constant at the level of 10% accuracy, which requires precise measurement of the distances. It uses various methods to measure distance for instance SNe Ia, Tully-Fisher relation, surface-brightness fluctuations etc. In the fifth chapter we apply Δ statistic to the HST Key Project data in order to check the presence of non-Gaussian and direction dependent features. Our results show that although this data set seems to be free of direction dependent features, it is inconsistent with the Gaussian errors. Analytic Marginalization : The quantities of real interest in cosmology are ΩM and ΩΛ, Hubble constant could in principle be treated as a nuisance parameter. It would be useful to marginalize over the nuisance parameter. Although it can be done numerically using Bayesian method, Δ statistic does not allow it. In chapter six we propose a method to marginalize over H0 analytically. The χ2 in this case is a complicated function of errors in the data. We compare this analytic method with the Bayesian marginalization method and results show that the two methods are quite consistent. We apply the Δ statistic to the SNe data after the analytic marginalization. Results do not change much indicating the insensitivity of the direction de-pendent features to the Hubble constant. A variation to the Δ statistic: As has been discussed earlier that, it is difficult to calculate the theoretical distribution of Δ in general. However if the parent distribution follows certain conditions it is possible to derive the analytic form for the Gumbel distribution for Δ. In the seventh chapter we derive a variation to the Δ statistic in a way that allows us to calculate the analytic distribution. The results in this case are different from those presented earlier, but they confirm the same direction dependence and non-Gaussian features in the data.