Cosmological perturbation theory (CPT) is an important tool with which inhomogeneities that seed the observed structure of our universe can be studied. This thesis introduces the subject of CPT and discusses applications of this at both linear and second order. At linear order the evolution of the curvature perturbation around horizon crossing is examined. We study single field inflation models numerically, and compare the curvature perturbation at horizon crossing to that at the end of inflation. In addition, linear-order CPT is extended to the case of a multi-fluid system and an approximation for the velocities of the baryons and photons in the early universe as well as the strength of the electric field is found. We use second order CPT to study magnetogenesis. By using fully relativistic, non-linear CPT we show how magnetic fields are generated. This is done by presenting the first fully analytical calculation of the magnetic field at second order. Our results suggest that magnetic fields with strengths of the order of 10²⁷G and with scale dependence M ∝ k⁴ may be generated - findings which are largely in agreement with previous numerical results. We end by outlining possible extensions to this work, in particular related to the study of primordial magnetogenesis.

In this thesis we present research into linear perturbations in Lemaître-Tolman-Bondi (LTB) and Assisted Coupled Quintessence (ACQ) Cosmologies. First we give a brief overview of the standard model of cosmology. We then introduce Cosmological Perturbation Theory (CPT) at linear order for a at Friedmann-Robertson-Walker (FRW) cosmology. Next we study linear perturbations to a Lemaître-Tolman-Bondi (LTB) background spacetime. Studying the transformation behaviour of the perturbations under gauge transformations, we construct gauge invariant quantities in LTB. We show, using the perturbed energy conservation equation, that there is a conserved quantitiy in LTB which is conserved on all scales. We then briefly extend our discussion to the Lemaître spacetime, and construct gauge-invariant perturbations in this extension of LTB spacetime. We also study the behaviour of linear perturbations in assisted coupled quintessence models in a FRW background. We provide the full set of governing equations for this class of models, and solve the system numerically. The code written for this purpose is then used to evolve growth functions for various models and parameter values, and we compare these both to the standard CDM model and to current and future observational bounds. We also examine the applicability of the "small scale approximation", often used to calculate growth functions in quintessence models, in light of upcoming experiments such as SKA and Euclid. We nd the results of the full equations deviates from the approximation by more than the experimental uncertainty for these future surveys. The construction of the numerical code, Pyessence, written in Python to solve the system of background and perturbed evolution equations for assisted coupled quintessence, is also discussed.

We propose and construct a two-parameter expansion around a Friedmann-Lemaitre- Robertson-Walker geometry which uses both large-scale and small-scale perturbations analogous to cosmological perturbation theory and post-Newtonian gravity. We justify this observationally, derive a set of field equations valid on a fraction of the horizon size and perform a detailed investigation of the associated gauge problem. We find only the Newtonian gauge, out of the standard gauges used in cosmological perturbation theory, is applicable to post-Newtonian perturbations; we can identify a consistent set of perturbed quantities in the matter and gravity sectors and construct corresponding gauge-invariant quantities. The field equations, written in terms of these quantities, takes on a simpler form, and allows the effects of small-scale structure on the large-scale properties of the Universe to be clearly identified and discussed for different physical scenarios. With a definition of statistical homogeneity, we find that the cosmological constant and the average energy density, of radiation and dust, source the Friedmann equation, whereas only the inhomogeneous part of the Newtonian energy density sources the Newton-Poisson equation { even though both originate from the same equation. There exists field equations at new orders in our formalism, such as a frame-dragging field equation a hundred times larger than expected from using cosmological perturbation theory alone. Moreover, we find non-linear gravity, mode-mixing and a mixing-of-scales at orders one would not expect from intuition based on cosmological perturbation theory. By recasting the field equations as an effective fluid we observe that these non-linearities lead to, for example, a large-scale effective pressure and anisotropic stress. We expect our formalism to be useful for accurately modelling our Universe, and for investigating the effects of non-linear gravity in the era of ultra-large-scale surveys.

We consider a recent approach to the construction of gauge-invariant relational observables in gravity in the context of cosmological perturbation theory. These observables are constructed using a field-dependent coordinate system, which we take to be geodesic lightcone coordinates. We show that the observables are gauge-independent in the fully nonlinear theory, and that they have the expected form when one adopts the geodesic lightcone gauge for the metric. We give explicit expressions for the Sasaki-Mukhanov variable at linear order, and the Hubble rate — as measured both by geodesic observers and by observers co-moving with the inflaton — to second order. Moreover, we show that the well-known linearised equations of motion for the Sasaki-Mukhanov variable and the scalar constraint variables follow from the gauge-invariant Einstein’s equations

One of the exciting aspects of cosmology is to understand the period of `cosmic inflation' that powered the epoch of the Big Bang. Inflation has been very successful in explaining several puzzles of the standard big bang scenario. But the most important success of inflation is that it can explain the temperature fluctuations of cosmic microwave background and the large scale structures of the universe. Despite its great success, the details of the physics of inflation are still unknown. A large number of models of inflation successfully explain all the observations making it remarkably hard to distinguish between different models. We explore the possibility of differentiating between different inflationary models by studying two-point and three-point functions of primordial fluctuations produced during inflation. First, we explore possible constraints on the inflationary equation state by considering current measurements of the power spectrum. Next, we explore the possibility of a single field slow-roll inflationary model with general initial state for primordial fluctuations. The two-point and three-point functions of primordial fluctuations are generally computed assuming that the fluctuations are initially in the Bunch-Davies state. However, we show that the constraints on the initial state from observed power spectrum and local bispectrum are relatively weak and for slow-roll inflation a large number of initial states are consistent with the current observations. As the precision of the observations is increasing significantly, we may learn more about the initial state of the fluctuations in the near future. Finally, we explore the consistency relations for the three-point functions, in the squeezed limit, of scalar and tensor perturbations in single-field inflation that in principle can be used to differentiate between single-field and multi-field inflation models. However, for slow-roll inflation, we find that it is possible to violate some of the consistency relations for initial states that are related to the Bunch-Davies state by Bogoliubov transformations and we identify the reason for the violation. Then we discuss the observational implications of this violation. / text

One of the most pressing, modern cosmological mysteries is the cause of the accelerated expansion of the universe. The energy density required to cause this large scale opposition to gravity is known to be both far in excess of the known matter content, and remarkably smooth and unclustered across the universe. While the most commonly accepted answer is that a cosmological constant is responsible, alternatives abound. This thesis is primarily concerned with such alternatives; both their theoretical nature and observational consequences. In this thesis, we will dedicate Chapter 1 to a brief review on the fundamentals of general relativity, leading into the basics of theoretical cosmology. Following this we will recall some of the key observations that has lead to the standard CDM cosmology. The standard model has well known problems, many of which can be answered by the theoretical ideas of inflation. In Chapter 2 we explore these ideas, including a summary of classical field theory in the context of cosmology, upon which inflation is based. This also serves as the groundwork for Chapter 3, where the varied models of dark energy (and their motivations) are discussed - many of which are also reliant on field theory (such as quintessence). These notions are combined in a model described in Chapter 4, where we describe our own addition to a scenario that unifies dark energy and inflation. This addition - involving a coupling of the inflation field to an additional one - alter the way reheating takes place after inflation, removing some of the shortcomings of the original proposal. The analysis is extended in Chapter 5, to include the effect of quantum corrections. There we show that although a cursory analysis indicates a coupling between quintessence and some other field does not necessarily give rise to dangerously large quantum corrections, provided the effects of decoupling are taken into account. We move on in Chapter 6 to examine the basics of cosmological perturbation theory, and derive the general equations of motion for density and velocity perturbations for a system of fluids, allowing for the exchange of energy-momentum. We make use of this in Chapters 7 and 8, were we examine the growth of structure in a universe where energy is exchanged between dark matter and dark energy. In particular, in Chapter 7 we see that a particular form of the interaction can lead to an instability in the early universe, and we derive the condition for this to be the case. In Chapter 8, we discuss how a similar interaction can lead to a mimicry of modified gravity, and relate this directly to cosmological observations. Finally we summarise our conclusions and discuss avenues of future research in Chapter 9.

We deal with cosmological perturbation theory in my work. We investigate General Theory of Relativity in Higher Dimensions in the Chapter 1. I mention GHP-formalism and algebraical classification of spacetimes. I use spinors to show that spacetimes of dimension 4 are special. I discuss also Kundt spacetimes, which are interesting for perturbation theory of black holes. I work with perturbations of FLRW ST's in GHP formalism in Chapter 2, which we want to use in Cosmological Inflation. The final part of my thesis is connected with scalar perturbations in f(R)-cosmologies, that can be used for explaining accelerated expansion in the last 5 billion years. I investigate the Universe at the scales of 150 Mpc, where I could not use the hydrodynamical approach. Thus I work with the generalization of the Landau's mechanical approach. I need quasi-static approximation for getting the potentials Φ and Ψ, since the equations are too complicated for direct integration. I plan to use the result also for numerical simulation of motions of dwarf galaxies in these potentials. Powered by TCPDF (www.tcpdf.org)

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18070号 / 理博第3948号 / 新制||理||1569(附属図書館) / 30928 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 佐々木 節, 教授 田中 貴浩, 教授 畑 浩之 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

Early Universe physics leaves distinct imprints on the Cosmic Microwave Background (CMB) and Large-Scale Structure (LSS). The current cosmological paradigm to explain the origin of the structures we see in the Universe today (CMB and LSS), named Inflation, says that the Universe went through a period of accelerated expansion. Density fluctuations that eventually have grown into the temperature fluctuations of the CMB and the galaxies and other structures we see in the LSS come from the quantization of the scalar field (inflaton) which provokes the accelerated expansion. The most simple inflationary model, which contains only one slowly-rolling scalar field with canonical kinetic term in the action, produces a power-spectrum (Fourier transform of the two-point correlation function) approximately scale invariant and an almost null bispectrum (Fourier transform of the three-point correlation function). This characteristic is called Gaussianity, once random fields that follow a normal distribution have all the odd moments null. Yet, more complex inflationary models (with more scalar fields and/or non-trivial kinetic terms in the action, etc) and possible alternatives to inflation have a non-vanishing bispectrum which can be parametrized by a non-linearity parameter f_NL, whose value differs from model to model. In this work we studied the basic ingredients to understand such statements and focused on the observational evidences of this parameters and how the current and upcoming galaxy surveys are able to impose constraints to the value of f_NL with a better accuracy, through the multi-tracer technique, than those obtained by means of CMB measurements. / A física do Universo primordial deixa sinais distintos na Radiação Cósmica de Fundo (CMB) e Estrutura em Larga Escala (LSS). O paradigma atual da cosmologia explica a origem das estruturas que vemos hoje (CMB e LSS) através da inflação, teoria que diz que o Universo passou por um período de expansão acelerada. As flutuações de densidade que eventualmente crescem, dando origem às flutuações de temperatura da CMB, às galáxias e outras estruturas que vemos na LSS, provém da quantização do campo escalar (inflaton) que provoca a tal expansão acelerada. O modelo inflacionário mais simples, o qual contém um único campo escalar nas condições de rolamento lento e termo cinético canônico da ação, possui o espectro de potências (transformada de Fourier da função de correlação de dois pontos) aproximadamente invariante de escala e o bispectro (transformada de Fourier da função de correlação de três pontos) aproximadamente nulo. Tal característica é conhecida por Gaussianidade, uma vez que campos aleatórios cuja distribuição é uma normal tem todas as funções de correlação de ordem ímpar nulas. Contudo, modelos inflacionários mais complexos (mais campos escalares, termos cinéticos não-triviais na ação, etc) e alternativas possíveis à inflação possuem um bispectro não nulo, o qual pode ser parametrizado através do parâmetro de não-linearidade f_NL, cujo valor difere de modelo para modelo. Neste trabalho estudamos os ingredientes básicos para entender tais afirmações e focamos nas evidências observacionais desse parâmetro e como os levantamentos de galáxias atuais e futuros podem impor restrições ao valor de f_NL com uma precisão maior, através da técnica de múltiplos traçadores, do que aquelas obtidas com medidas da CMB.

Early Universe physics leaves distinct imprints on the Cosmic Microwave Background (CMB) and Large-Scale Structure (LSS). The current cosmological paradigm to explain the origin of the structures we see in the Universe today (CMB and LSS), named Inflation, says that the Universe went through a period of accelerated expansion. Density fluctuations that eventually have grown into the temperature fluctuations of the CMB and the galaxies and other structures we see in the LSS come from the quantization of the scalar field (inflaton) which provokes the accelerated expansion. The most simple inflationary model, which contains only one slowly-rolling scalar field with canonical kinetic term in the action, produces a power-spectrum (Fourier transform of the two-point correlation function) approximately scale invariant and an almost null bispectrum (Fourier transform of the three-point correlation function). This characteristic is called Gaussianity, once random fields that follow a normal distribution have all the odd moments null. Yet, more complex inflationary models (with more scalar fields and/or non-trivial kinetic terms in the action, etc) and possible alternatives to inflation have a non-vanishing bispectrum which can be parametrized by a non-linearity parameter f_NL, whose value differs from model to model. In this work we studied the basic ingredients to understand such statements and focused on the observational evidences of this parameters and how the current and upcoming galaxy surveys are able to impose constraints to the value of f_NL with a better accuracy, through the multi-tracer technique, than those obtained by means of CMB measurements. / A física do Universo primordial deixa sinais distintos na Radiação Cósmica de Fundo (CMB) e Estrutura em Larga Escala (LSS). O paradigma atual da cosmologia explica a origem das estruturas que vemos hoje (CMB e LSS) através da inflação, teoria que diz que o Universo passou por um período de expansão acelerada. As flutuações de densidade que eventualmente crescem, dando origem às flutuações de temperatura da CMB, às galáxias e outras estruturas que vemos na LSS, provém da quantização do campo escalar (inflaton) que provoca a tal expansão acelerada. O modelo inflacionário mais simples, o qual contém um único campo escalar nas condições de rolamento lento e termo cinético canônico da ação, possui o espectro de potências (transformada de Fourier da função de correlação de dois pontos) aproximadamente invariante de escala e o bispectro (transformada de Fourier da função de correlação de três pontos) aproximadamente nulo. Tal característica é conhecida por Gaussianidade, uma vez que campos aleatórios cuja distribuição é uma normal tem todas as funções de correlação de ordem ímpar nulas. Contudo, modelos inflacionários mais complexos (mais campos escalares, termos cinéticos não-triviais na ação, etc) e alternativas possíveis à inflação possuem um bispectro não nulo, o qual pode ser parametrizado através do parâmetro de não-linearidade f_NL, cujo valor difere de modelo para modelo. Neste trabalho estudamos os ingredientes básicos para entender tais afirmações e focamos nas evidências observacionais desse parâmetro e como os levantamentos de galáxias atuais e futuros podem impor restrições ao valor de f_NL com uma precisão maior, através da técnica de múltiplos traçadores, do que aquelas obtidas com medidas da CMB.