从动力学系统视角对宇宙学模型的定性分析
Qualitative Analysis of Cosmological Models Using Dynamical System Perspective
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中文总结 AI 辅助
论文从动力学系统视角研究宇宙学模型，通过回顾背景知识，研究f(Q)引力中的多种宇宙学模型，包括耗散查普利金气体、DBI暗能量、规范标量场等，利用多种观测数据和分析方法，对模型进行约束和分析，总结结果并展望未来研究。
中文摘要 AI 辅助
本论文研究宇宙加速的理论和观测方面，聚焦暗能量模型和修正引力框架。目标是分析其可行性、动力学行为和微扰稳定性，以识别能描述宇宙加速膨胀的模型。第1章回顾广义相对论等背景知识。第2章研究f(Q)引力中的耗散查普利金气体宇宙学。第3章用高斯过程通过哈勃和DESI观测重建狄拉克-玻恩-英费尔德（DBI）暗能量动力学。第4章用动力学系统分析重合f(Q)引力中的规范标量场宇宙学。第5章将动力学分析扩展到f(Q)引力中的DBI标量场。第6章研究标量场在背景和微扰水平的演化。第7章总结主要结果及未来研究范围。附录包含场方程等数学细节。
英文摘要
This thesis investigates theoretical and observational aspects of cosmic acceleration, focusing on dark energy models and modified gravity frameworks. The goal is to analyse their viability, dynamical behaviour, and perturbative stability to identify models capable of describing the accelerated expansion of the Universe. Chapter 1 reviews the essential background General Relativity, and mathematics of teleparallel and symmetric teleparallel geometries, basic cosmological models, matter components, and the key observational probes. The chapter concludes with a summary of modified gravity theories, including f(R), f(T) and f(Q). Chapter 2 studies a dissipative Chaplygin gas cosmology in f(Q) gravity. The model is constrained using the CC and Pantheon+SH0ES dataset, and its performance is assessed through information criteria and diagnostic tools such as Om and statefinder analysis. Chapter 3 reconstructs the dynamics of Dirac-Born-Infeld (DBI) dark energy using Hubble and DESI observations via Gaussian Processes. The reconstructed potential is fitted to theoretical models using chi-square and MCMC techniques, giving constrains on DBI scalar field. Chapter 4 analyses canonical scalar-field cosmology in coincident f(Q) gravity using dynamical systems. Chapter 5 extends the dynamical analysis to the DBI scalar field in f(Q) gravity. Chapter 6 examines scalar-field evolution at both background and perturbation levels. Perturbation equations for key gauge invariant variables are derived, and an extended phase space combining background and perturbation dynamics is constructed. Finally, chapter 7 summarizes the main results along with scope for future research. Further mathematical details including derivation of field equation and cosmology equations and foundational issues related to f(Q) gravity are compiled in the following four sections: Appendix A, Appendix B, Appendix C and Appendix D.
