We explore the mechanics of inflation within simplified extra-dimensional models involving an inflaton interacting with a Einstein-Maxwell system in two extra dimensions. The models are complicated enough to include a stabilization mechanism for the extra-dimensional radius, but simple enough to solve the full six-dimensional field equations. After performing a consistent truncation, which guarantees our six-dimensional equations are equivalently satisfied by the four dimensional equations of motion, we explore (numerically and analytically) the power-law solutions evident in our initial parameter search. After a comprehensive search for potential power-law scaling solutions in both six and four dimensions, we find two that give rise to interesting inflationary dynamics. They both can generically exist outside of the usual four dimensional effective theory, and yet, we still trust them since our truncation is consistent. One of these is a dynamical attractor whose features are relatively insensitive to initial conditions, but whose slow-roll parameters cannot be arbitrarily small; the other is not an attractor but can roll much more slowly, until eventually transitioning to another solution due to its unstable nature. We present a numerical and analytic discussion of these two solutions. Four of the appendices contain calculations in more explicit detail than are performed in the main text, while a fifth contains a representative Mathematica worksheet and the sixth contains the general results of the systematic sweep for scaling solutions. / Thesis / Master of Science (MSc) / When looking out at the night sky, we see a universe that is extremely flat and looks the same no matter what direction we stare. However, these present-day observations require the universe to have begun under very specific circumstances, which is not something that naturally occurs; think about what is necessary to hit a hole-in-one with a golf club: a very precise and specific shot is required. The theory of Cosmological Inflation—a period of rapid expansion in the early universe—is the current leading theory proposed to explain these observations. In our exploration, we aim to study inflation from a higher-dimensional perspective in which two extra spatial dimensions are added to our usual three. Ultimately, we find three classes of solutions, two of which exist outside of the regimes usually studied, that have the potential both to explain current observations, and also be useful tools in future explorations.

In this thesis we consider four different topics in the field of cosmology, namely, black hole topology, the averaging problem, the effect of surface terms on the dynamics of classical and quantum fields, and the generation of an open universe through inflation with random initial conditions. It should be mentioned that while the research for this thesis was being done, no large effort was made to pursue a single theme. One reason for the diversity of the topics in this thesis is that the results which came out of this research were not always the results which were expected to be found when the investigation was started. Another reason for looking at several topics is simply that once a problem has been solved, then it is natural to move on to another problem which has not yet been solved. For those readers who value that a thesis is centred around a single unifying theme, let me mention that each of the four topics in this thesis are indeed related. Namely, each topic which we discuss focuses on an aspect of the global dynamics of the universe, in a situation where this is non-trivially different from the local dynamics. The non-trivial relation between global and local dynamics is rarely addressed in cosmology. Partially this is because of the difficulties which arise when one considers a realistic universe with infinitely many coupled degrees of freedom. Hence, it is a common practice to rely on simplifications which reduce the number of degrees of freedom, or the couplings between them. Further, there are few direct observations which probe the large-scale dynamics of the universe, or none at all, depending on the length scale and the type of cosmological model which one considers. As a consequence, there is a considerable freedom in choosing a priori assumptions or simplifications in the field of cosmology, without being able to falsify the validity thereof. For instance, when we analyse the relation between field perturbations at spatial infinity and perturbations here and now, we assume that quantum field theory, as we know it, is valid everywhere between here and spatial infinity. Although one cannot avoid making certain fundamental assumptions, the type of simplifications which are adopted in a calculation plays a less fundamental role. It is the objective of this thesis to improve our understanding of the large-scale dynamics of the universe by showing rigorously what one can and what one cannot derive from certain fundamental assumptions. Interestingly, our results are often quite different from the results which are based on the same assumptions, but which involve certain commonly made simplifications as well. This thesis is structured as follows. In the first chapter it is shown how different sections of the Kruskal geometry can be identified in a way which preserves time-orient ability of the spacetime. The existence of topologically different but locally identical solutions of Einstein's equations is well known, and not surprising considering the differential structure of these equations. also discuss the occurrence of Hawking radiation in topologically different black-hole geometries. Furthermore, we study the relation between black-hole solutions and circular cosmic strings. Assuming the existence of circular 1 cosmic string with deficit angle ranging between 0 and 211", we are able to construct a class of non-trivial vacuum solutions with properties similar to black-hole solutions but with a more complicated topology. In the second chapter of this thesis, we focus on the averaging problem in cosmology. The averaging problem occurs when one attempts to model a realistic inhomogeneous universe by a more symmetric model. Although averaging is often implied when studying realistic cosmological models, a rigorous treatment of averaging in cosmology appears to be surprisingly difficult. One difficulty which occurs when one tries to specify an averaging procedure is related to the large number of unphysical degrees of freedom which are present in the problem, namely, the coordinate freedom and the gauge freedom. The coordinate freedom manifests itself when one tries to evaluate the average of tensorial quantities, since the components of a tensor depend on the local choice of a frame. One may attempt to avoid this problem by specifying a local frame and evaluating some kind of average for each component separately. However, since there is no choice of frame which is preferred for physical reasons, this gives rise to a considerable amount of ambiguity. When one follows a perturbative approach, there is an additional freedom of choosing a gauge, which makes it ambiguous what one means by a perturbation of a physical quantity, even when this quantity does not depend on the local choice of frame. By specifying a choice of gauge, it becomes well defined what one means by a perturbation, but once again no choice of gauge seems to be preferred for physical reasons. In addition to these problems, there is an inherent ambiguity which is related to the freedom in choosing an averaging operation. Since there is generally more than one choice of averaging operation which is mathematically consistent, one needs to impose additional constraints which restrict the freedom of choosing an averaging operation. However, one would like to do so on the basis of a minimal set of assumptions. It is shown that each of these problems can be resolved in the case where perturbations theory can be applied. We use our results to calculate the lowest order non-trivial correction to the expansion of the observable universe, which is due to the fact that averaging does not commute with evaluating the (nonlinear) Einstein equations. In the third chapter of this thesis, we investigate the relation between surface terms which are evaluated at spatial infinity, and the local dynamics of a scalar field. Starting from the path-integral approach to quantum field theory, it is shown that the contribution of surface terms to the variation of the action functional cannot in general be neglected. The classical field equations can be derived by requiring that the variation of the action vanishes for all field perturbations, and it is shown that a surface term generally contributes a non-trivial source term to the classical field equations. This source term appears to vanish in spatially flat geometries, but it diverges in a spatially open geometries with super curvature perturbations. Rather surprisingly, it appears that the degrees of freedom of the scalar field which generate surface terms must have zero norm in the space of square integrable field 2 perturbations. Without restricting these zero-norm degrees of freedom, it follows that the local dynamics of the field are sensitive to details of the spacetime at spatial infinity. The main difficulty which we are confronted with consists of quantifying the zero-norm degrees of freedom. We briefly discuss a strategy for resolving this problem. In the fourth chapter we discuss different types of inflation. As is well known, the standard idea of inflation provides a simple explanation for the homogeneity of the observed universe. However, it appears to be much less straightforward to reconcile a period of inflation with the observed negative spatial curvature in the universe. Bubble inflation combines these two aspects, but it requires a rather restricted type of potential. After introducing the established ideas of standard inflation and bubble inflation, we focus on the dynamics of bubble spacetimes. It is shown that the often used thin-wall approach is not consistent with the assumption that the stress-energy is generated by a scalar field, although this assumption plays a crucial role in the theory of bubble-dynamics. In order to resolve this problem, we derive a simplified set of equations which describe the exact dynamics of a general spherically symmetric bubble spacetime. We then focus on the question of whether the restrictions on the shape of the potential, which are essential in the bubble inflation scenario, are necessary in order to explain the generation of negative spatial curvature during inflation. By studying the most generic situation where constant-scalar field hypersurfaces make a transition from being spacelike to being time like , it is shown that negative spatial curvature is generated under conditions which are more generic than the conditions which are generally assumed. The results which are presented in this thesis have been obtained through independent research, which was conducted by the author on an individual basis. The contents of the first three chapters have been published, [1] - [3], excluding the third section of the first chapter, which was added recently. The contents of the last chapter are currently being prepared for submission. None of the results which are obtained in this thesis have, to the best of my knowledge, been published elsewhere, or the original work has been cited.

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The redshift drift of objects moving in the Hubble flow has been proposed as a powerful model-independent probe of the underlying cosmology. A measurement of the first- and second-order redshift derivatives appears to be well within the reach of upcoming surveys using as the Extremely Large Telescope high resolution spectrometer (ELT-HIRES) and the Square Kilometer Phase 2 Array (SKA). Here we show that an unambiguous prediction of the R-h = ct cosmology is zero drift at all redshifts, contrasting sharply with all other models in which the expansion rate is variable. For example, multiyear monitoring of sources at redshift z = 5 with the ELT-HIRES is expected to show a velocity shift Delta v = -15 cm s(-1) yr(-1) due to the redshift drift in Planck I > CDM, while Delta v = 0 cm s(-1) yr(-1) in R-h = ct. With an anticipated ELT-HIRES measurement error of +/- 5 cm s(-1) yr(-1) after 5 yr, these upcoming redshift drift measurements might therefore be able to differentiate between R-h = ct and Planck I > CDM at similar to 3 sigma, assuming that any possible source evolution is well understood. Such a result would provide the strongest evidence yet in favour of the R-h = ct cosmology. With a 20-yr baseline, these observations could favour one of these models over the other at better than 5 sigma.

This work aims to understand how cosmic inflation embeds into larger models of particle physics and string theory. Our work operates within a weakened version of the Landscape paradigm, wherein it is assumed that the set of possible Lagrangians is vast enough to admit the notion of a generic model. By focusing on slow-roll inflation, we examine the roles of both the scalar potential and the space of couplings which determine its precise form. In particular, we focus on the structural properties of the scalar potential, and find a surprising result: inflection point inflation emerges as an important —and under certain assumptions, dominant — possibility in the context of generic scalar potentials. We begin by a systematic coarse graining over the set of possible inflection point inflation models using V.I. Arnold’s ADE classification of singularities. Similar to du Val’s pioneering work on surface singularities, these determine structural classes for inflection point inflation which depened on a distinct number of control parameters. We consider both single and multifield inflation, and show how the various structural classes embed within each other. We also show how such control parameters influence the larger physical models in to which inflation is embedded. These techniques are then applied to both MSSM inflation and KKLT-type models of string cosmology. In the former case, we find that the scale of inflation can be entirely encoded within the super- potential of supersymmetric quantum field theories. We show how this relieves the fine-tuning required in such models by upwards of twelve orders of magnitude. Moreover, unnatural tuning between SUSY breaking and SUSY preserving sectors is eliminated without the explicit need for any hidden sector dynamics. In the later case, we discuss how structural stability vastly generalizes — and addresses — the Kallosh-Linde problem. Implications for the spectrum of SUSY breaking soft terms are then discussed, with an emphasis on how they may assist in constraining the inflationary scalar potential. We then pivot to a general discussion of the FLRW-scalar phase space, and show how inflection points induce caustics — or dynamical fixed points — amongst the space of possible trajectories. These fixed points are then used to argue that for uninformative priors on the space of couplings, the likelihood of inflection point inflation scales with the inverse cube of the number of e-foldings. We point out the geometric origin for the known ambiguity in the Liouville measure, and demonstrate of inflection point inflation ameliorates this problem. Finally we investigate the effect of the fixed point structure on the spectrum of density perturbations. We show how an anomaly in the Cosmic Mircowave Background data — low power at large scales — can be explained as a by product of the fixed point dynamics.

The task which I set myself when I undertook to study the text of the Greater Bundahisn was at that time by no means clear either in its difficulty or its extent. Nor could I then know to what degree the increased knowledge of Iranian, in particular, of Middle Iranian, the period from about 300 B.C. to 900 A.D., had made understanding of this text possible. Iranian studies attained to a new birth when in 1904 the results of archaeological expeditions to central Asia were first made known. By these discoveries of MSS the difficulties of reading Pahlavi were at once lightened. It was certain that if the vocabulary of Western Persia of Sasanian times were fully known, the Zoroastrian Pahlavi texts could no longer hide their secrets under the cursive alphabet which had hindered the progress of earlier scholars. Not only the Western dialects but also the recently discovered Sogdian and Saka have naturally enriched our understanding of the Middle Iranian vocabulary. But the lack of complete indexes of the words of theses two dialects still renders their use difficult. For Saka, besides the published indexes (of which the most important has only just appeared in Sten Konow's Saka Studies) I made my own index of all the unindexed Saka so far published. For Sogdian there has been the grammar of Buddhist Sogdian by R. Gauthiot, besides which I have had some indexed material of my own. Reichelt's promised glossary of Buddhist Sogdian has not yet appeared. The few Manichean Sogdian texts so far published (by F.W.K. Miller and Waldschmidt-Lentz) have yielded interesting words. For the Christian Sogdian there is the index in F.W.K. Muller's Soghdische Texte.

Orientador: Pedro Cunha de Holanda / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-22T08:38:27Z (GMT). No. of bitstreams: 1 Boriero_DanielFrancisco_D.pdf: 1994859 bytes, checksum: a59e512b9fdcb71d04bb5f9702f0fb60 (MD5) Previous issue date: 2013 / Resumo: Cosmologia de neutrinos é a atividade de pesquisa dedicada ao teste de propriedades de neutrinos através de observáveis cosmológicos. Particularmente, as propriedades estudadas e testadas ao longo desta tese de doutorado foram à massa dos neutrinos e o número de estados estéreis. Ambas as propriedades são motivadas pela observação em experimentos terrestres do fenômeno de oscilação entre estados de interação. Diferentemente da existência de estados massivos, os indícios da existência de estados estéreis são tenuemente sugeridos, contudo ambas as propriedades representariam um grande impacto no modelo cosmológico caso sejam observados sinais positivos de suas existências e por esse motivo justificam-se suas análises. A utilização da cosmologia como um laboratório de física de neutrinos é possível graças à imensa abundância de neutrinos remanescentes do universo primordial além da sensibilidade sem precedentes das observações realizadas. Telescópios e detectores em planejamento ou em implementação supostamente alcançarão a sensibilidade equivalente aos valores mínimos das massas determinados pelo fenômeno de oscilação. A perspectiva de tais sensibilidades experimentais deve ser acompanhada pelo aumento equivalente da precisão obtida nas previsões teóricas dos efeitos pelos quais pretende-se detectar a presença de neutrinos massivos ou de estados estéreis. Nesta tese de doutorado, além de ser detalhadamente desenvolvida a teoria e a metodologia convencionais na análise de dados cosmológicos para obtenção de medidas ou limites para estes dois parâmetros, também foram desenvolvidos métodos para aumentar a precisão da previsibilidade teórica. Foram abordados dois desafios teóricos prementes, a imprecisão das previsões no regime não-linear de perturbação para neutrinos massivos e a degenerescência em relação aos parâmetros de modelos cosmológicos estendidos. As melhorias obtidas não compõem soluções definitivas, mas sim metodologias a serem desenvolvidas sistematicamente ao longo da obtenção de novos dados reais e simulados. / Abstract: Neutrino cosmology is the research activity dedicated to test neutrino properties by cosmological observables. Specially, the properties studied and tested along this graduate research were the neutrino mass and the sterile states. Both properties are motivated from observations in terrestrial experiments of the phenomenon of oscillation between interaction states. Differently from the existence of massive states, the signals of sterile states are weakly suggested, however both properties would mean a sizeable impact in the cosmological model in case any positive signal is detected and, therefore, their analysis are justified. The utilization of cosmology as a laboratory of neutrino physics is possible thanks to the high abundance of remaining neutrinos from the primordial universe, besides the unprecedented sensitivity of experimental observations. Telescopes and detectors planned or under construction will supposedly reach the sensitivity equivalent to the minimal neutrinos masses given by the oscillation phenomenum. The perspective of such experimental sensitivities must be followed by the equivalent improvement in the theoretical predictability for the effects with which it is intended to detect a positive signal of massive neutrinos or sterile states. In this Ph.D. Thesis, besides being developed in detail the theory and methodology used in the analysis of cosmological data to measure or constrain these two parameters, we also developed methods and tools to improve the theoretical predictability. Two pressing theoretical challenges were addressed, the imprecision of the predictions in the non-linear regime of perturbations for massive neutrinos and the degeneracy related to parameters of extended cosmological models. The improvements obtained do not make up a definitive solution, but rather methodologies to be systematically developed along with the achivement or the eventuality of new real and simulated data. / Doutorado / Física / Doutor em Ciências

One focus of research in cosmology regards the growth of structure in the universe: how we end up with stars, galaxies, galaxy clusters, and large scale structure in a universe that appears homogeneous and isotropic on large scales. Using cosmological perturbation theory, we investigate the evolution of density and velocity perturbations corresponding to a universe that is slowly contracting (Ijjas and Steinhardt), testing with and comparing different values for the equation-of-state parameter. This allows for the comparison of the growth of large scale structure in scenarios including a matter-dominated expanding universe, a dark energy-dominated expanding universe, and now, an ekpyrotic scalar field-dominated contracting universe. Further, we consider the timescales on which deviations from ΛCDM in favor of the model considered could become relevant.

Quantum mechanics is usually formulated in terms of a single Hilbert space and observables are defined as operators on this space. Attempts to describe entire spacetimes and their resident matter in this way often encounter paradoxes. For example, it has been argued that an observer falling into a black hole may be able to witness deviations from unitary, violations of semi-classical quantum field theory, and the like. This thesis argues that the essential problem is the insistence on the use of a single, global Hilbert space, because in general it may be that a physical observer cannot causally probe all of the information described by this space due to the presence of horizons. Instead, one could try to define unitary quantum physics directly in terms of the information causally accessible to particular observers. This thesis makes steps toward a systematization of this idea. Given an observer on a timelike worldline, I construct coordinates which (in good cases) cover precisely the set of events to which she can send and then receive a signal. These coordinates have spatial sections parametrized by her proper time, and the metric manifestly encodes the equivalence principle in the sense that it is flat along her worldline. To describe the quantum theory of fields according to these observers, I define Hilbert spaces in terms of field configurations on these spatial sections and show how to implement unitary time-evolution along proper time. I explain how to compare the observations of a pair of observers, and how to obtain the description according to some particular observer given some a priori global description. In this sense, the program outlined here constructs a manifestly unitary description of the events which the observer can causally probe. I give a number of explicit examples of the coordinates, and show how the quantum theory works for a uniformly accelerated observer in flat spacetime and for an inertial (co-moving) observer in an inflating universe. / text

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