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

Orientadores: Alex Eduardo de Bernardini, Marcelo Moraes Guzzo / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataglin / Made available in DSpace on 2018-08-17T16:24:26Z (GMT). No. of bitstreams: 1 DuartePerico_EderLeonardo_M.pdf: 2896271 bytes, checksum: 3596fcdea9450fe936e36e96d5ffbad3 (MD5) Previous issue date: 2011 / Resumo: O assunto deste estudo é formação de estruturas em grandes escalas em um universo plano dominado por radiação, matéria escura fria e constante cosmológica como modelo de energia escura no caso particular de presença de um gás degenerado de férmions (GDF) não interagentes como fluído de teste. Nosso modelo admite uma evolução linear das perturbações cosmológicas como também se limita a perturbações escalares, responsáveis pela formação de estruturas. O objetivo principal é analisar a contribuição do GDF no espectro de potências da matéria no presente após uma evolução isentrópica das perturbações primordiais, e compará-la com resultados obtidos para neutrinos cosmológicos. Neste caso, teremos uma mudança contínua de comportamento do GDF de gás ultra-relativístico para não relativístico, o qual aconteceria durante o período de domínio da matéria. Com o objetivo de obter expressões analíticas para a evolução temporal das perturbações do GDF tivemos que fazer o estudo destas em quatro casos diferentes: no período de domínio da radiação, no período de domínio da matéria escura, na escala de super-horizonte durante a transição entre estes dois períodos, e finalmente no período de domínio da constante cosmológica. Fomos bem sucedidos ao chegar a resultados consistentes utilizando dois caminhos diferentes: no primeiro, usando a equação de conservação do tensor momento energia para um gás ideal de férmions totalmente degenerado e não interagente, e no segundo, usando a equação de Boltzmann para um gás de férmions fortemente degenerado e também não interagente. Os dois métodos analíticos levam à mesma solução para as perturbações do GDF quanto escritas até primeira ordem em teoria de perturbações. De forma complementar, os nossos resultados numérico mostram um aumento no espectro de potências da matéria para escalas intermediárias se comparado com a contribuição dos neutrinos massivos. Finalmente estendemos nossa análise numérica ao substituirmos a matéria escura fria CDM e a constante cosmológica por um gás generalizado de Chaplygin GCG como modelo efetivo para o setor escuro do universo, mantendo as condições de contorno que envolvem as densidades médias, e as condições iniciais para as perturbações / Abstract: The subject of this study is the formation of large scale structures (LSS) in a at universe dominated by radiation, cold dark matter and cosmological constant - as a dark energy model - in presence of a degenerate fermionic gas (GDF) as non-interacting test fluid. Our model assumes a linear evolution of cosmological perturbations as well as merely scalar perturbations responsible for structure formation. Our main objective is to analyze the contribution of the GDF in the matter power spectrum today, after an isentropic evolution of primordial perturbations and a continuous change of behavior of ultra-relativistic for non-relativistic GDF, which occurs during the matter domination era in our model. To obtaining analytical expressions for temporal evolution of the GDF perturbations we did study them in four different cases: during the radiation domination era, the dark matter domination, the super-horizon scale limit during the transition between these first two periods and finally during the cosmological constant domination era. We get these results using two different approaches: first, using the conservation equation of the stress-energy tensor for a perfect and non-interacting and fully degenerated fermionic gas, and second, using the Boltzmann equation for a non-interacting and strongly degenerated fermionic gas. Both methods lead to the same analytical solution for GDF perturbations at first order on perturbation theory. On the other hand, our numerical results show an increase in the power spectrum of matter for intermediate scales if compared it with the contribution of massive neutrinos. Finally, we show the change on the results of the standard model of cosmology (CDM) when we exchanging the cold dark matter CDM and the cosmological constant for a generalized Chaplygin gas GCG how effective model of twice old fluids with the same mean density of energy / Mestrado / Cosmologia / Mestre em Física

<p>Karakteristika hiperboličnih sistema zakona odrržanja je da čak i u slučaju glatkog po-četnog uslova re&scaron;enja uglavnom razvijaju prekide u konačnom vremena. Zbog toga se posmatraju slaba re&scaron;enja koja dati sistem zadovoljavaju u distributivnom smislu i mogu biti čak i neograničena &scaron;to se ispoljava kroz pojavu Dirakove delta funkcije u re&scaron;enju. U ovoj disertaciji se akcenat stavlja na analizu protoka sti&scaron;ljivog neviskoznog fluida koji ne menja pravac prilikom kretanja. Protok je opisan Ojlerovim sistemom iz gasne dinamike koji se sastoji iz zakona održanja mase, količine kretanja i energije, dok su karakteristike fluida određene konstitutivnim relacijama. U slučaju izentropskog ili izotermnog protoka sistem se svodi na zakone održanja mase i količine kretanja. Glatka re&scaron;enja takvog sistema automatski zadovoljavaju zakon održanja energije, dok prelaskom na slabu formulaciju dolazi do gubitka energije. Za predstavnike sistema gasne dinamike sa nepozitivnim pritiskom su uzeti sistem gasne dinamike bez pritiska i model za&nbsp; Čapliginov gas i njegova uop&scaron;tenja. Data su re&scaron;enja Rimanovih problema za te sisteme koja se mogu predstaviti kao kombinacija klasičnih elementarnih talasa i senka talasa koji aproksimiraju re&scaron;enja u obliku delta udarnih talasa i koji omogućavaju re&scaron;avanje početnog problema koji u početnom uslovu sadrži delta funkciju. Na primeru modela za uop&scaron;ten Čapliginov gas dokazano je da uslov prekompresivnosti nije jači od entropijskog uslova, &scaron;to je prvi takav rezultat u literaturi. Dalje su kori&scaron;ćena re&scaron;enja Rimanovih problema, kao i problema singularne interakcije i dat je algoritam za konstrukciju globalnog dopustivog približnog re&scaron;enja početnog problema za sistem gasne dinamike bez pritiska. Algoritam je univerzalan i ideja se može pro&scaron;iriti na veliki broj sistema zakona održanja i veliki broj početnih uslova. Diskutovane su promene energije u približnom re&scaron;enju i posle interakcija. Dobijeno približno re&scaron;enje slabo konvergira u prostoru Radonovih mera sa predznakom.</p> / <p>&nbsp;</p><p class="MsoNormal">A solutions to hyperbolic conservation laws systems starting out as smooth often develop singularities in a finite time. As a consequence, we are forced to look for weak solutions that satisfy the system in distributional sense. Those solutions are often unbounded, which is expressed through the appearance of Dirac delta function. In this theses we study a one-dimensional, compressible and inviscid flow of a fluid. The process is described by compressible Euler gas dynamics system which consists of conservation laws of mass, linear momentum and energy, while the characteristics of the fluid are described using constitutive relations. In the case of isentropic or isothermal flow the system reduces to conservation laws of mass and linear momentum. The energy is conserved for smooth solutions to such systems, but while passing to the weak formulation the energy is being dissipated. As representatives, we&nbsp; consider pressureless gas dynamics system, as well as Chaplygin gas model and its generalizations. We give the solutions to Riemann problems which can be represented as a combinations of classical elementary waves and shadow waves that approximate the solutions in the form of delta shock and allow as to solve the problems with initial data containing delta function. We use generalized Chaplygin gas model as demonstration of the fact that overcompressibility condition is not stronger that entropy condition, which is the first result of that kind in the literature. Further, we use solutions&nbsp; to the Riemann problems, as well as singular interaction problems to give the algorithm for construction of global admissible approximate solution to the pressureless gas dynamics initial value problem. The algorithm is universal and idea can be applied to large number of conservation laws systems and large number of initial data. We discuss&nbsp; energy changes in approximate solution and after the interactions. The constructed approximate solution converges in the space of signed Radon measures.</p><p><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:TrackMoves/> <w:TrackFormatting/> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:DoNotPromoteQF/> <w:LidThemeOther>EN-US</w:LidThemeOther> <w:LidThemeAsian>X-NONE</w:LidThemeAsian> <w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> <w:SplitPgBreakAndParaMark/> <w:DontVertAlignCellWithSp/> <w:DontBreakConstrainedForcedTables/> <w:DontVertAlignInTxbx/> <w:Word11KerningPairs/> <w:CachedColBalance/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> <m:mathPr> <m:mathFont 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