Cosmological perturbation theory is crucial for our understanding of the universe. The linear theory has been well understood for some time, however developing and applying the theory beyond linear order is currently at the forefront of research in theoretical cosmology. This thesis studies the applications of perturbation theory to cosmology and, specifically, to the early universe. Starting with some background material introducing the well-tested 'standard model' of cosmology, we move on to develop the formalism for perturbation theory up to second order giving evolution equations for all types of scalar, vector and tensor perturbations, both in gauge dependent and gauge invariant form. We then move on to the main result of the thesis, showing that, at second order in perturbation theory, vorticity is sourced by a coupling term quadratic in energy density and entropy perturbations. This source term implies a qualitative difference to linear order. Thus, while at linear order vorticity decays with the expansion of the universe, the same is not true at higher orders. This will have important implications on future measurements of the polarisation of the Cosmic Microwave Background, and could give rise to the generation of a primordial seed magnetic field. Having derived this qualitative result, we then estimate the scale dependence and magnitude of the vorticity power spectrum, finding, for simple power law inputs a small, blue spectrum. The final part of this thesis concerns higher order perturbation theory, deriving, for the first time, the metric tensor, gauge transformation rules and governing equations for fully general third order perturbations. We close with a discussion of natural extensions to this work and other possible ideas for off-shooting projects in this continually growing field.
Closing the Observational Gap in Cosmic Dynamics: AI-Enabled Reconstruction of the Universe's Vorticity and Rotational Flow Morphology
School of Physics and Astronomy, Sun Yat-Sen University（中山大学物理学院）；Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院紫金山天文台）；School of Astronomy and Space Sciences, University of Science and Technology of China（中国科学技术大学天文与空间科学学院）；South-Western Institute for Astronomy Research, Yunnan University（云南大学西南天文研究所）；Korea Institute of Advanced Studies (KIAS)（韩国高等科学研究院）；Institute for Astronomy, University of Edinburgh（爱丁堡大学天体物理研究所）；Peng Cheng Laboratory（鹏城实验室）；Institute for Astronomy, The school of Physics, Zhejiang University（浙江大学物理学院天体物理研究所）；Center for Cosmology and Computational Astrophysics, Zhejiang University（浙江大学宇宙学与计算天体物理学中心）；CSST Science Center for the Guangdong–Hong Kong–Macau Greater Bay Area, SYSU（中山大学粤港澳大湾区嫦娥科学中心）
