As teorias de gravitação invariante por escala propõem uma variação com relação ao tempo da constante gravitacional ou da massa dos objetos que constituem o universo. Desta forma a intensidade da interação gravitacional também se torna variável, modificando sensivelmente o comportamento do universo. Algumas teorias foram propostas no decorrer do século, porém, descartadas devido a problemas técnicos e de concordância com dados observacionais. trabalho a ser apresentado nesta dissertação está fundamentado em uma teoria de gravitação invariante por escala, a qual vem atualmente sendo desenvolvida e é denominada teoria penta-dimensional Espaço-Tempo-Massa. Tal teoria propõe a quantidade de massa de repouso como uma quantidade extensiva, de maneira a introduzi-la na métrica e torná-la variável. Diversos trabalhos foram realizados com esta teoria, incluindo alguns, o estudo de modelos cosmológicos. Investigaremos aqui a extensão do modelo cosmológico de Bianchi tipo V, que é um dos mais importantes modelos do universo. Duas métricas foram propostas e as soluções das equações de campo da teoria SD-Espaço-Tempo-Massa para tais métricas foram obtidas. Tais soluções correspondem a espaços não-planos. Um estudo sobre singularidades na métrica e na curvatura foi realizado para ambas as métricas, em adição, o tensor de energia-momento induzido foi obtido para as métricas e as suas propriedades investigadas. Através da análise do tensor de Kretschmann verificou-se a ausência de singularidades efetivas nos modelos 5D abordados, sugerindo uma distribuição finita de energia devido a inclusão da massa de repouso. / The scale invariant gravitational theories propose the time variation either in the gravitational constant or in the rest mass of the objects that constitute the universe. By this way the intensity of the gravitational interaction varies as well, changing accordingly the behavior of the universe. Several theories have been proposed in the literature, however most of them have been discharged due to drawbacks in thecnicalities or lack of agreement with observational data. The work conducted here takes into account a 5-dimensional theory called SpaceTime- Mass, which proposes that the rest mass be na extensible quantity that change with time. Severa! investigations have been done so far with this theory, some o f them including cosmological studies. Here we will investigate the 5D extension of the Bianchi type V cosmological model, which is one of the most important model of the universe. Two metrics are proposed and the solution of the corresponding 5D-Spae-Time-Mass field equations are found. Both solutions shown to be non-flat spaces. The singularity behavior of the metric and curvature were done, the induced energy-momentum tensor for both metrics were determined and their properties were investigated. Through the analysis of the Kretschmann tensor, it has been shown that there is no effective singularity in the space, which suggest that there is a finite distribution of energy due to the inclusion of the rest mass variable.

As teorias de gravitação invariante por escala propõem uma variação com relação ao tempo da constante gravitacional ou da massa dos objetos que constituem o universo. Desta forma a intensidade da interação gravitacional também se torna variável, modificando sensivelmente o comportamento do universo. Algumas teorias foram propostas no decorrer do século, porém, descartadas devido a problemas técnicos e de concordância com dados observacionais. trabalho a ser apresentado nesta dissertação está fundamentado em uma teoria de gravitação invariante por escala, a qual vem atualmente sendo desenvolvida e é denominada teoria penta-dimensional Espaço-Tempo-Massa. Tal teoria propõe a quantidade de massa de repouso como uma quantidade extensiva, de maneira a introduzi-la na métrica e torná-la variável. Diversos trabalhos foram realizados com esta teoria, incluindo alguns, o estudo de modelos cosmológicos. Investigaremos aqui a extensão do modelo cosmológico de Bianchi tipo V, que é um dos mais importantes modelos do universo. Duas métricas foram propostas e as soluções das equações de campo da teoria SD-Espaço-Tempo-Massa para tais métricas foram obtidas. Tais soluções correspondem a espaços não-planos. Um estudo sobre singularidades na métrica e na curvatura foi realizado para ambas as métricas, em adição, o tensor de energia-momento induzido foi obtido para as métricas e as suas propriedades investigadas. Através da análise do tensor de Kretschmann verificou-se a ausência de singularidades efetivas nos modelos 5D abordados, sugerindo uma distribuição finita de energia devido a inclusão da massa de repouso. / The scale invariant gravitational theories propose the time variation either in the gravitational constant or in the rest mass of the objects that constitute the universe. By this way the intensity of the gravitational interaction varies as well, changing accordingly the behavior of the universe. Several theories have been proposed in the literature, however most of them have been discharged due to drawbacks in thecnicalities or lack of agreement with observational data. The work conducted here takes into account a 5-dimensional theory called SpaceTime- Mass, which proposes that the rest mass be na extensible quantity that change with time. Severa! investigations have been done so far with this theory, some o f them including cosmological studies. Here we will investigate the 5D extension of the Bianchi type V cosmological model, which is one of the most important model of the universe. Two metrics are proposed and the solution of the corresponding 5D-Spae-Time-Mass field equations are found. Both solutions shown to be non-flat spaces. The singularity behavior of the metric and curvature were done, the induced energy-momentum tensor for both metrics were determined and their properties were investigated. Through the analysis of the Kretschmann tensor, it has been shown that there is no effective singularity in the space, which suggest that there is a finite distribution of energy due to the inclusion of the rest mass variable.

We show that Einstein’s gravitational field equations for the Friedmann- Robertson-Lemaître-Walker (FRLW) and for two conformal versions of the Bianchi I and Bianchi V perfect fluid scalar field cosmological models, can be equivalently reformulated in terms of a single equation of either generalized Ermakov-Milne- Pinney (EMP) or (non)linear Schrödinger (NLS) type. This work generalizes or presents an alternative to similar reformulations published by the authors who inspired this thesis: R. Hawkins, J. Lidsey, T. Christodoulakis, T. Grammenos, C. Helias, P. Kevrekidis, G. Papadopoulos and F.Williams. In particular we cast much of these authors’ works into a single framework via straightforward derivations of the EMP and NLS equations from a simple linear combination of the relevant Einstein equations. By rewriting the resulting expression in terms of the volume expansion factor and performing a change of variables, we obtain an uncoupled EMP or NLS equation that is independent of the imposition of additional conservation equations. Since the correspondences shown here present an alternative route for obtaining exact solutions to Einstein’s equations, we reconstruct many known exact solutions via their EMP or NLS counterparts and show by numerical analysis the stability properties of many solutions.

This thesis consists of three articles investigating the asymptotic behaviour of cosmological spacetimes with symmetries arising in Mathematical General Relativity. In Paper A and B, we consider spacetimes with Bianchi symmetry and where the matter model is that of a perfect fluid. We investigate the behaviour of such spacetimes close to the initial singularity ('Big Bang'). In Paper A, we prove that the Strong Cosmic Censorship conjecture holds in non-exceptional Bianchi class B spacetimes. Using expansion-normalised variables, we further show detailed asymptotic estimates. In Paper B, we prove similar estimates in the case of stiff fluids. In Paper C, we consider T2-symmetric spacetimes satisfying the Einstein equations for a non-linear scalar field. To given initial data, we show global existence and uniqueness of solutions to the corresponding differential equations for all future times. In the special case of a constant potential, a setting which is equivalent to a linear scalar field on a background with a positive cosmological constant, we investigate in detail the asymptotic behaviour towards the future. We prove that the Cosmic No-Hair conjecture holds for solutions satisfying an additional a priori estimate, an estimate which we show to hold in T3-Gowdy symmetry. / Denna avhandling består av tre artiklar som undersöker det asymptotiska beteendet hos kosmologiska rumstider med symmetrier som uppstår i Matematisk Allmän Relativitetsteori. I Artikel A och B studerar vi rumstider med Bianchi symmetri och där materiemodellen är en ideal fluid. Vi undersöker beteendet av sådana rumstider nära ursprungssingulariteten ('Big Bang'). I Artikel A bevisar vi att den Starka Kosmiska Censur-förmodan håller för icke-exceptionella Bianchi klass B-rumstider. Med hjälp av expansions-normaliserade variabler visar vi detaljerade asymptotiska uppskattningar. I Artikel B visar vi liknande uppskattningar för stela fluider. I Artikel C betraktar vi T2-symmetriska rumstider som uppfyller Einsteins ekvationer för ett icke-linjärt skalärfält. För givna begynnelsedata visar vi global existens och entydighet av lösningar till motsvarande differentialekvationer för all framtid. I det speciella fallet med en konstant potential, en situation som motsvarar ett linjärt skalärfält på en bakgrund med en positiv kosmologisk konstant, undersöker vi i detalj det asymptotiska beteendet mot framtiden. Vi visar att den Kosmiska Inget-Hår-förmodan håller för lösningar som uppfyller en ytterligare a priori uppskattning, en uppskattning som vi visar gäller i T3-Gowdy-symmetri. / <p>QC 20171220</p>

Whereas contemporary debates in Latin American studies addressing sovereignty often focus on dictatorships and the transitions to democratic governments in Latin America in the late twentieth century, Sovereignties Displaced: Avant-Garde Prose and Authoritarianism in Spain, Chile, and Argentina (1923-1936) adopts a transatlantic framework and directs critical attention to the cultural production of the interwar period. The historical and cultural events preceding and following 1929 are connected to World War I, the political crisis of democratic systems, and the global socioeconomic instability of the period. The three countries studied in the present work would be affected by these conditions, sharing an almost synchronic development of the authoritarian governments of Miguel Primo de Rivera in Spain (1923-1930), of Carlos Ibáñez del Campo in Chile (1927-1931), and José Félix Uriburu in Argentina (1930-1932). Additionally, the rise of authoritarianism and the decay of parliamentary institutions characterizing this epoch condition and inscribe the political essays and avant-garde novels composed by the intellectuals and writers analyzed in this study: from Spain, María Zambrano (1904-1991), Ramón Gómez de la Serna (1888-1963), and Benjamín Jarnés (1888-1949); from Chile, Alberto Edwards Vives (1874-1932), Juan Emar (1893-1964), and Vicente Huidobro (1893-1948); and from Argentina, Ramón Doll (1896-1970), Norah Lange (1905-1972), and Roberto Arlt (1900-1942). It should be noted that while considering national circumstances, my argumentation is divided into sections organized not by country, but rather by subject matter: a methodological and theoretical introduction, three analytical chapters, and concluding remarks. Established critical assessments of the avant-gardes, as offered by experts like Renato Poggioli (1907-1963), have underscored that democratic forms of government would provide the initial conditions of possibility of the historical avant-gardes. Other scholars, however, have recognized the interdependency of early twentieth century artistic discourses, revolutionary ideas, and authoritarianism. Informed by the theorization of sovereignty and democracy of Jacques Derrida (1930-2004), and the concept of community of Roberto Esposito (1950-), my research examines, in political essays and vanguard novels, the opposition of individual vis-à-vis collective forms of rule. The texts of my corpus manifest a recurrent concern relating to the tension between self-rule and collective-rule, a dynamic which organizes and destabilizes avant-garde formations themselves. Consequently, I analyze the philosophical and political ramifications of these authors’ defense, negation, or destabilization of the individual-collective opposition in the context of the deterioration of parliamentarism. In my first chapter, I examine the following essays that represent a range of political positions from the interwar years: Horizonte del liberalismo (1930) by María Zambrano, Liberalismo en la literatura y la política (Con una segunda edición de: “Democracia mal menor”) (1934, n/d) by Ramón Doll, and La fronda aristocrática en Chile (1928) by Alberto Edwards Vives. Framed by the sociological assessments of José Ortega y Gasset in La rebelión de las masas (1930), this chapter considers these essayists’ observations regarding mass politics and the role of political and economic elites. I foreground the ethical problems relating to these authors’ conceptions of the human subject and their concomitant formulations of governance, deriving from various ideological orientations. The essayists’ comparable anxieties regarding the limits of democratic politics reveal the complexities of the period and serve as a springboard for the subsequent chapters that study the politics of avant-garde novels. In my second chapter, shifting from essayistic discourse to vanguard fiction, I analyze philosophical oppositions central to the configuration of sovereignty, and to the theory and practice of democracy. These tensions organize various components of the following novels: Un año (1935) by Juan Emar (pseudonym of Álvaro Yáñez Bianchi), 45 días y 30 marineros (1933) by Norah Lange, and El caballero del hongo gris (1928) by Ramón Gómez de la Serna. I demonstrate that, although these narratives do not contain explicit references to the emergence of authoritarianism and the erosion of parliamentarism of the period, these narratives are structured by problems that have implications for a thinking of issues relating to sovereignty and democracy. These novels similarly present how individuals interact with groups, such that it becomes imperative to consider the political consequences of these relations in order to critique, for example, fraternalistic and nationalistic notions of political filiation. My final chapter studies the narrative presentations of radical political projects that aim to restructure society in Los siete locos (1929) by Roberto Arlt, La próxima (1934) by Vicente Huidobro, and Lo rojo y lo azul (1932) by Benjamín Jarnés. In contrast to the narratives included in the second chapter, these avant-garde novels establish an explicit dialogue with the conditions of crisis of the interwar years. From insurrections and utopian settlements, to revolutionary military revolts, these narrations depict small vanguard groups that propose various plots that seek to radically reshape the social order. Even though poetry is often positioned as the paradigmatic form of vanguard literary expression, my research theorizes the understudied phenomenon of Hispanic avant-garde prose. In particular, I account for the variation among avant-garde novels of the period, by sustaining that there are gradations of vanguard narrative depending on different factors that range from the transparency or opacity of linguistic expression, to the organization of the narrative material. In this sense, some novels considered vanguardist, while approaching a certain radicality in terms of language and form, may incorporate elements of the realist-naturalist novelistic tradition. Likewise, I assert the importance of attending to the varied uses of meta-reflexive procedures in Hispanic vanguard prose. Given their implicit and explicit interaction with contemporary historical conditions and political and artistic discourses of the 1920s and 1930s, I contend that the essays and avant-garde novels analyzed offer a fertile ground to examine the nature of sovereignty, while also presenting, in some crucial instances, potential images of what a democracy worthy of this name could look like. / Spanish