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Exploring Modified Gravity : From Gauss-Bonnet to Stringy Gravity

  • 이호철 (Hocheol Lee, 서강대학교 일반대학원)

초록 (요약문)

This thesis explores cosmology based on Gauss-Bonnet gravity and Double Field Theory as modifications and alternatives to General Relativity and the ΛCDM model. While General Relativity and ΛCDM have successfully explained many cosmic phenomena, they fall short of fully understanding the nature of dark matter and dark energy, which constitute about 95% of the Universe. This gap indicates the need for new theoretical frameworks. Consequently, this thesis investigates Gauss-Bonnet gravity and Double Field Theory as forms of modified gravity. The Dilatonic Einstein-Gauss-Bonnet theory includes the Gauss-Bonnet term, a quadratic form of curvature. From this, the equations of motion are derived, and black hole solutions with their properties are obtained, featuring an arbitrary scalar field that contrasts with the conventional no-hair theorem. This theory is also applied to the early Universe to describe changes in the thermal decoupling scenarios of WIMP. Furthermore, in the Double Field Theroy, the closed string massless sector is treated as a stringy gravitation field. This approach leads to new Friedmann equations. The solutions to these equations are obtained both analytically and numerically, and with observational data, the present Universe is an open Universe undergoing accelerated expansion without any dark sector in Double Field Theory.

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초록 (요약문)

본 논문은 일반 상대성 이론과 ΛCDM 모델의 수정 및 대안으로써, 가우스-보네 중력과 이중장론에 기반한 우주론을 기술한다. 기존의 일반 상대성 이론과 ΛCDM이 많은 우주 현상을 성공적으로 설명했지만, 우주의 약 95%에 해당하는 암흑 물질과 암흑 에너지의 본질을 완전히 파악하지 못하고 있는 점은 새로운 이론의 필요성을 시사하고 있다. 이에 본 논문은 수정 중력의 일환으로 가우스-보네 중력과 이중장론을 연구한다. 딜라톤 아인슈타인-가우스-보네 이론은 이차 곡률 항인 가우스-보네 항을 포함한다. 이로부터 운동 방정식을 유도하고, 기존의 무모 정리에 반하는, 임의의 스칼라장이 존재하는 독특한 블랙홀의 해와 그 성질을 구한다. 이를 초기 우주에도 적용하여 암흑 물질의 열적 분리 시나리오 변화를 서술한다. 한편, 이중장론에서는 닫힌 끈을 중력장으로써 기술한다. 이를 통해 새로운 프리드만 방정식을 유도한다. 방정식의 해를 해석 및 수치적으로 구하고 관측 데이터와 결합하여 이중장론에서 현재 우주는 암흑 물질 혹은 암흑 에너지 없이 가속 팽창하는 열린 우주임을 보인다.

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목차

1 Introduction 1
2 Hairy Black Holes in Dilatonic Einstein-Gauss-Bonnet Theory 5
2.1 Review: Gauss-Bonnet Gravity 6
2.2 Review: No-Hair Theorem 7
2.2.1 Novel No-Hair Theorem 8
2.2.2 New No-Hair Theorem 13
2.2.3 Simple No-Hair Theorem 16
2.3 Non-Minimally Coupled Action with negative cosmological constant and Gauss-Bonnet Term 19
2.4 Near Horizon Behavior 22
2.5 Asymptotic Behavior 26
2.6 Shifting and Rescaling 27
2.7 Numerical Solutions of Hairy Black Holes 29
2.7.1 Black Holes in AdS-Like Spacetime 30
2.7.2 Black Holes in AdS-Like Spacetime with Varying γ 34
2.8 Non-Vanishing Boundary Term 36
3 WIMPs in Dilatonic Einstein-Gauss-Bonnet Cosmology 38
3.1 Review: Dark Matter Relics 39
3.2 Non-Minimally Coupled Action with Gauss-Bonnet Term in Early Universe 46
3.3 WIMP Relic Density 52
3.4 Indirect Detection Bounds on WIMP Annihilation 55
3.5 Numerical Solutions of Friedmann Equations 57
3.6 Constraints on the DEGB Scenario 71
3.6.1 Black Hole and Neutron Star Binaries 71
3.6.2 WIMP Indirect Detection 75
4 Late-Time Cosmology in Double Field Theory 80
4.1 Review: Einstein Double Field Equations 82
4.2 Review: Friedman Equations in Double Field Theory 85
4.3 Astrophysical Tests and Data 87
4.4 Accelerating Open Universe in String Frame 88
4.5 Bayesian Inference from Observational Data 91
4.6 Exact Vacuum Free of Coincidence Problem 95
4.7 Confronting with the Observations 99
4.8 Bouncing Open Universe 101
5 Conclusion and Discussion 103
Appendix A Useful Properties in General Relativity 107
Appendix B Variation of Gauss-Bonnet Term 108
B.1 Variation of q()R^2 108
B.2 Variation of q()R_{ν}R^{ν} 109
B.3 Variation of q()R_{νρσ}R^{νρσ} 109
B.4 Derivation of T^{GB}_{ν} 111
Appendix C Explicit Expression of Second-Order Coupled Differential Equations 113
Appendix D Vacuum Solutions in Double Field Theory 117
References 126

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