京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第22245号 / 理博第4559号 / 新制||理||1655(附属図書館) / 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 田中 貴浩, 教授 川合 光, 教授 向山 信治 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

The vacuum of quantum field theory is not empty space but filled with quantum vacuum fluctuations, which give rise to many intriguing effects. The first part of this Thesis addresses cosmic inflation, where the quantum fluctuations of the inflaton field freeze and get amplified in the expanding universe. Afterwards, we turn our attention towards Bose-Einstein condensates, a laboratory system. Since most of our calculations are performed using a mean-field expansion, we will study the accuracy of a finite-range interaction potential onto such an expansion. Exploiting the universality of quantum fluctuations, several aspects of cosmic inflation will be identified in ballistically expanding Bose-Einstein condensates. The effective action technique for calculating the quantum backreaction will be scrutinized. Finally, we consider dynamic quantum phase transitions in the last part of this Thesis. To this end two specific scenarios will be investigated: firstly, the structure formation during the superfluid to Mott-insulator transition in the Bose-Hubbard model; and secondly, the formation of spin domains as a two-dimensional spin-one Bose gas is quenched from the (polar) paramagnetic to the (planar) ferromagnetic phase. During this quench, the symmetry of the ground state is spontaneously broken and vortices (topological defects) form.

Submitted by Liliane Ferreira (ljuvencia30@gmail.com) on 2018-08-21T12:44:31Z No. of bitstreams: 2 Dissertação - Lucas Elias Vieira - 2018.pdf: 1438523 bytes, checksum: 81df75730e0ab41f69b4619af81cd7a2 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2018-08-22T12:42:43Z (GMT) No. of bitstreams: 2 Dissertação - Lucas Elias Vieira - 2018.pdf: 1438523 bytes, checksum: 81df75730e0ab41f69b4619af81cd7a2 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2018-08-22T12:42:43Z (GMT). No. of bitstreams: 2 Dissertação - Lucas Elias Vieira - 2018.pdf: 1438523 bytes, checksum: 81df75730e0ab41f69b4619af81cd7a2 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2018-07-13 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work, we study topological defects in classical field theory aiming applications in cosmology. Topological and non-topological solutions were investigated in two dimensions, where we also analyzed the stability of some of these. We consider models of one and two real scalar fields, whose solutions were obtained via quadrature, BPS and orbit methods. The stability of these solutions also were investigated in some cases. In order to apply scalar field theory in cosmology, we revisit some topics of general relativity, such that the principle of equivalence, Einstein's field equations and Schwarzschild's solution for Einstein's equation. We also present some topics in cosmology, relevant to the present work, such that the cosmological principle, Hubble's law and cosmological inflation. We discuss the solutions of the Einstein's equations in the FRW metric in the so-called Hot Big Bang model-the universe composed of matter and radiation. In order to solve some problems of initial conditions of the universe, we introduce the inflationary theory, which supposes that the primordial universe was underwent an accelerated expansion guided by a scalar field. In sequence, we introduce the standard cosmological model, which states that the universe is in accelerated expansion driving by a cosmological constant, named dark energy, which constitutes about seventy percent of the universe energy. Finally, we present a first order formalism for cosmology and discuss two model describing the standard and tachyonics dynamics for scalar field that represent the dark energy. / Neste trabalho foram abordadas soluções do tipo defeitos topológicos em teoria clássica de campos. Foram investigadas soluções topológicas e não topológicas em duas dimensões, onde também analisamos a estabilidade de algumas destas. Consideramos modelos de um e dois campos escalares reais, onde utilizamos os métodos de quadratura, BPS e das órbitas para obter soluções. Com o intuito de aplicar a teoria de campos escalares em cosmologia, introduzimos a teoria da relatividade geral, falando sobre o princípio da equivalência, equações de campo de Einstein e solução de Schwarzschild para as equações de Einstein. Abordamos alguns tópicos em cosmologia, onde enunciamos o princípio cosmológico, lei de Hubble e inflação cosmológica. Resolvemos as equações de Einstein na métrica FRW considerando o universo composto de matéria e radiação denominado modelo Big Bang quente. Com o objetivo de resolver alguns problemas de condições iniciais do universo, introduzimos a teoria inflacionária, a qual propõe que o universo primordial sofreu uma expansão acelerada guiada por um campo escalar. Após mostrar como a teoria da inflação corrige tais problemas, apresentamos o modelo cosmológico padrão, o qual afirma que o universo está em expansão acelerada e utiliza uma constante cosmológica como guia da expansão, tal constante neste cenário representa a denominada energia escura que compõe aproximadamente setenta por cento do universo. Finalmente, nós apresentamos o formalismo de primeira ordem para cosmologia e discutimos dois modelos descrevendo dinâmicas padrão e taquiônica para o campo escalar, representando a energia escura.

The vacuum of quantum field theory is not empty space but filled with quantum vacuum fluctuations, which give rise to many intriguing effects. The first part of this Thesis addresses cosmic inflation, where the quantum fluctuations of the inflaton field freeze and get amplified in the expanding universe. Afterwards, we turn our attention towards Bose-Einstein condensates, a laboratory system. Since most of our calculations are performed using a mean-field expansion, we will study the accuracy of a finite-range interaction potential onto such an expansion. Exploiting the universality of quantum fluctuations, several aspects of cosmic inflation will be identified in ballistically expanding Bose-Einstein condensates. The effective action technique for calculating the quantum backreaction will be scrutinized. Finally, we consider dynamic quantum phase transitions in the last part of this Thesis. To this end two specific scenarios will be investigated: firstly, the structure formation during the superfluid to Mott-insulator transition in the Bose-Hubbard model; and secondly, the formation of spin domains as a two-dimensional spin-one Bose gas is quenched from the (polar) paramagnetic to the (planar) ferromagnetic phase. During this quench, the symmetry of the ground state is spontaneously broken and vortices (topological defects) form.

Astrophysical observations of the cosmic microwave background point to inconsistencies in the standard model of cosmology, and a primordial accelerated expansion of the universe known as inflation has been suggested as a solution. Unfortunately, observational evidence of inflation is lacking, and there exists hundreds of models that populate the inflationary landscape. In this thesis, we explore three of these and see what constraints are set on them in order to account for observations. We find that two of the models have regimes of trans-planckian nature, while the third leads to a non-invertible equation. / Astronomiska observationer av den kosmiska bakgrundsstrålningen tyder på bristfälligheter i standardkosmologin, vilket har lett till förslaget om en accelererande expansion i de tidigaste skeden av universum känd som inflation. I avsaknaden av observationella bevis finns det numera hundratals inflationsmodeller, och i detta arbete kommer vi att rikta fokuset mot tre av dessa avvilka två visar sig överstiga transplanckianska värden medan den sista leder till en ekvation som inte är inverterbar.