Phenomenology of the Extreme Limits in our Universe = 우리 우주의 초극단에 대한 현상론 연구

다국어 초록 (Multilingual Abstract)

The universe spans an extraordinary range of energy scales, from the subatomic to the cosmological. This thesis explores the phenomenology of the universe at its most extreme limits, focusing on the physics of inflation and dark matter.

The first part of the dissertation is dedicated to the phenomenology of inflation, emphasizing both model-building aspects and observational signatures. I study inflationary scenarios where the Standard Model Higgs field plays the role of the inflaton, demonstrating that such models can lead to significant production of primordial black holes and stochastic gravitational waves. I examine inflationary models that incorporate higher-order curvature corrections to the Starobinsky R2 action, showing that the resulting inflationary observables are highly sensitive to the coefficients of these higher-order terms. Furthermore, I investigate composite inflationary frameworks, where the flatness of the potential is protected by the dynamics of a composite sector. I construct a concrete model featuring multiple scalar degrees of freedom arising from this sector, which naturally leads to a hybrid inflation scenario consistent with current CMB data.

The second part addresses dark matter, with emphasis on the ultralight regime. I focus on axion-like theories as representative candidates in this mass range and investigate non-perturbative gravitational effects induced by Euclidean wormholes alter their predictions. I develop an effective formalism to account for these gravitational corrections and show that a large non-minimal coupling to gravity can protect the axion quality. These corrections generically induce a potential for axion-like particles, and I analyze the parameter space where such particles can be abundantly produced, potentially accounting for the observed dark matter density.

국문 초록 (Abstract)

우리 우주는 미시적 스케일에서부터 우주적 구조에 이르기까지 극도로 넓은 에너지 스펙트럼을 아우른다. 이런 극단의 스케일은 여러 이론적/관측적 의문들을 수반하며, 동시에 고유한 현상들을 동반한다. 본 학위논문은 이러한 극한 스케일에서의 현상에 대한 이론적 이해를 목표로, 급팽창과 암흑물질 현상론 연구를 논의한다.

논문의 전반부는 고에너지 극한을 동반하는 급팽창 이론의 다양한 모델과 동반되는 관측적 특성을 분석한다. 먼저, 표준 모형의 힉스장을 급팽창에 도입한 힉스 인플레이션 계열에서 원시 블랙홀과 중력파 배경의 생성 및 관측 가능성을 제시한다. 더불어서, 급팽창 예측에 대한 고차 곡률 항의 영향을 탐구해 스타로빈스키 R2 이론에 대한 고차 보정 항의 계수 크기가 급팽창 관측량에 미치는 결정적인 영향을 정량적으로 분석한다. 전반부의 마지막으로는, 입자이론에서 도입되는 복합 이론을 급팽창에 도입해 급팽창 퍼텐셜의 평탄성 보호 메커니즘을 고찰하고, 동반되는 다수의 스칼라장을 포함한 구체적인 모델을 구성해 현재의 우주론적 관측과 일관된 하이브리드 급팽창 시나리오를 제안한다.

논문의 후반부에서는 암흑물질, 그 중 초경량 질량 영역 극한에 집중한다. 본 극한에서는 암흑물질이 결맞은 파동의 특성을 보유하며, 질량과 퍼텐셜은 근사 대칭성에 의해 보호된다. 본 논문은 이런 항을 동반하는 액시온 이론에 비섭동적 중력 효과가 주는 영향을 정량적으로 분석하는 유효이론 접근을 제시한다. 더불어서 큰 비최소 결합항의 계수가 액시온의 품질 문제를 완화할 수 있음을 보이며, 해당 기여들이 보편적인 액시온 유사 입자 이론에도 적용됨을 탐구한다. 마지막으로, 해당 비섭동 중력 효과가 우리 우주의 암흑물질을 설명하는 파라미터 공간을 식별한다.

목차 (Table of Contents)

• List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
• List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv
• Abstract in English . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
• 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
• 1.1. Broad Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
• 1.2. Physics of Inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
• 1.3. Inflationary Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
• 1.3.1. Chaotic inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
• 1.3.2. Higgs inflation and its extensions . . . . . . . . . . . . . . . . . . 7
• 1.3.3. Starobinsky R2 Inflation . . . . . . . . . . . . . . . . . . . . . . . 10
• 1.4. Observational Tests of Inflation . . . . . . . . . . . . . . . . . . . . . . . . 11
• 1.5. Dark Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
• 1.5.1. Dark Matter Landscape . . . . . . . . . . . . . . . . . . . . . . . . 15
• 1.6. Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
• 2. PBH and Stochastic GW Production From Higgs-R2 Inflation . . . . . . . 23
• 2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
• 2.2. Higgs-R2 action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
• 2.3. Background Inflaton Dynamics . . . . . . . . . . . . . . . . . . . . . . . 31
• 2.4. Inflationary Perturbation Dynamics . . . . . . . . . . . . . . . . . . . . . 33
• 2.5. Ultra-slow-roll regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
• 2.5.1. USR dynamics and PBH dark matter abundance . . . . . . . . . . 39
• 2.6. Tachyonic Instability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
• 2.6.1. Power spectrum & PBH production - Tachyonic Instability . . . . . 53
• 2.6.2. Generation of a Stochastic GW Background . . . . . . . . . . . . . 57
• 2.7. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
• 3. Beyond the Starobinsky Model of Inflation . . . . . . . . . . . . . . . . . . . 62
• 3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
• 3.2. Dual Scalar Theory of f(R) . . . . . . . . . . . . . . . . . . . . . . . . . 65
• 3.3. Inflation Selection Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
• 3.4. Starobinsky Inflation and Extensions . . . . . . . . . . . . . . . . . . . . . 67
• 3.4.1. Inflation with R3 corrections . . . . . . . . . . . . . . . . . . . . . 69
• 3.5. Reheating and Inflation Duration . . . . . . . . . . . . . . . . . . . . . . . 74
• 3.6. Unitarization of Higgs Inflation Beyond the Starobinsky Framework . . . . 75
• 3.7. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
• 4. Composite Hybrid Inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
• 4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
• 4.2. Composite Inflation Model . . . . . . . . . . . . . . . . . . . . . . . . . . 81
• 4.3. Single-Field Inflation: Effects of Anomalous Dimensions . . . . . . . . . . 85
• 4.4. Two-Field Hybrid Inflation: Inflationary Observables . . . . . . . . . . . . 88
• 4.4.1. Waterfall Transition : Tachyonic preheating . . . . . . . . . . . . . 92
• 4.4.2. Benchmark Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 94
• 4.5. Conclusions and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . 97
• 5. An Effective Approach for Axion Wormholes . . . . . . . . . . . . . . . . . 99
• 5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
• 5.2. Euclidean Wormholes for General Axion Models . . . . . . . . . . . . . . 101
• 5.2.1. The Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
• 5.2.2. Field-Dependent Wormhole Solutions in Axion Gravity . . . . . . 105
• 5.3. Representative Models with a Single Axion Field . . . . . . . . . . . . . . 109
• 5.3.1. Complex Scalar Model . . . . . . . . . . . . . . . . . . . . . . . . 109
• 5.3.2. Complex Scalar Models with an Additional Scalar Field . . . . . . 117
• 5.4. Conclusions and Outlooks . . . . . . . . . . . . . . . . . . . . . . . . . . 124
• 6. Addressing the Axion Quality Problem through a Non-Minimal Coupling
• within the Palatini Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . 126
• 6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
• 6.2. The Axion Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
• 6.3. Palatini formulation analysis . . . . . . . . . . . . . . . . . . . . . . . . . 130
• 6.3.1. Wormhole Solutions . . . . . . . . . . . . . . . . . . . . . . . . . 130
• 6.3.2. Addressing the Axion Quality . . . . . . . . . . . . . . . . . . . . 134
• 6.4. Conclusions and outlooks . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
• 7. Wormhole-Induced ALP Dark Matter . . . . . . . . . . . . . . . . . . . . . 138
• 7.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
• 7.2. Wormhole-Induced Mass for Axion-Like Particles . . . . . . . . . . . . . . 141
• 7.2.1. The Model : A U(1) Scalar with a Non-Minimal Coupling . . . . . 141
• 7.2.2. Wormhole Configuration . . . . . . . . . . . . . . . . . . . . . . 142
• 7.2.3. Induced ALP Mass . . . . . . . . . . . . . . . . . . . . . . . . . . 145
• 7.3. ALP DM Abundance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
• 7.3.1. Pre-inflationary Scenario . . . . . . . . . . . . . . . . . . . . . . 150
• 7.3.2. Post-inflationary Scenario . . . . . . . . . . . . . . . . . . . . . . 152
• 7.4. General Inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
• 7.5. Wormhole ALP DM in Radial Mode Inflation . . . . . . . . . . . . . . . . 160
• 7.6. Conclusions and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . 167
• 8. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
• A. Supplementary Material for Chapter 5 . . . . . . . . . . . . . . . . . . . . . 170
• A.1. Scalar Potential Contributions to the Axion Wormhole Action . . . . . . . 170
• References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
• Abstract in Korean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208