Our Cosmos: the past, the present and the future

了解我们的宇宙，从大爆炸的热起源到神秘的黑洞，是人类最令人振奋和雄心勃勃的努力之一。建立在我的小组过去记录的坚实基础上，我的研究计划的长期目标是结合高能物理，数学和数据科学的现代进步，从多管齐下，跨学科和创新的角度，结合理论和观察，解开我们的宇宙动力学。在理论方面，我计划从cuscuton引力的新视角来解决大爆炸奇点问题，这是我在2007年首次提出的一个理论，目前正在经历复兴。问题是，爱因斯坦的广义相对论预测了它自己在一个巨大的早期时刻（即大爆炸奇点）的崩溃。2018年，我和我的团队证明了一个由cuscuton引力产生的弹跳宇宙学，或者cuscuton弹跳，从早期的收缩阶段平稳过渡，可以避免这种崩溃，而不会出现困扰早期提议的任何病态，这可能是解决古老的宇宙学奇点问题的分水岭。该提议计划在这一成功的基础上，构建一个自洽且可测试的cuscuston弹跳理论，该理论可以预测宇宙结构的种子，检查其数学性质，并探索其与量子引力更基本范式的联系。在观测方面，我计划利用2017年获得诺贝尔物理学奖的引力波的突破性发现，设计一个系统的、新颖的框架来探索宇宙模型。例如，最近对宇宙膨胀率的测量已经成为一个有争议的话题，被称为哈勃张力，这个问题可以通过多信使天文学来解决。与之前的方法相比，我们的方法在统计上更严格，但更实用，用于交叉相关引力波暗警报和星系调查的推理方法，它基于贝叶斯正演模型。虽然我们刚刚完成了这个项目的基础工作，但这个提议的目的是探索它在下一代引力波和星系调查中的实际实施。这项提案是一个雄心勃勃的项目的延续，该项目采用跨学科和跳出常规的思维来推动宇宙学的前沿，并将加拿大置于科学发现的前沿。不同背景的学生和博士后研究人员是这个项目不可分割的一部分，他们相互合作，为探究、创新和包容的氛围做出贡献。与此同时，他们获得了宝贵且高度可转移的技能，从数学、数值和数据科学技能到分析思维和团队合作，使他们能够在从学术界到工业和金融的广泛职业生涯中取得成功并脱颖而出。

Understanding our Cosmos, from its hot origins in the Big Bang to its enigmatic lockboxes of Black Holes, is amongst the most exhilarating and ambitious human endeavours. Building upon a solid foundation of my group's past record, the long term objective of my research program is to combine modern advances in high energy physics, mathematics, and data science to unravel our Cosmological Dynamics, from a multi-pronged, interdisciplinary, and innovative perspective that combines theory and observation. On the theoretical front, I plan to tackle the Big Bang singularity problem from the novel perspective of cuscuton gravity, a theory that I first pioneered in 2007 and is currently experiencing a renaissance. The problem is that Einstein's theory of General Relativity anticipates its own breakdown at a colossal early moment, known as the Big Bang singularity. In 2018, my team and I proved that a bouncing cosmology generated by cuscuton gravity, or a Cuscuton Bounce, with a smooth transition from an earlier contracting phase can evade this breakdown without any of the pathologies that plague earlier proposals, a possible watershed for resolving the age-old cosmological singularity problem. This proposal plans to build upon this success, to construct a self-consistent and testable theory of cuscuton bounce that could predict the seeds of cosmic structures, examine its mathematical properties, and explore its connection to a more fundamental paradigm for Quantum Gravity. On the observational front, I plan to exploit the groundbreaking discovery of gravitational waves, which won the Physics Nobel prize in 2017, to design a systematic and novel framework to probe cosmological models. For example, the recent measurements of the expansion rate of the universe have become a topic of controversy, known as the Hubble tension, a problem that can be addressed through Multi-Messenger Astronomy. In contrast to prior approaches, ours is a more statistically rigorous, yet practical, inference methodology for cross-correlating gravitational wave dark sirens and galaxy surveys, which is based on Bayesian forward modelling. While we have just wrapped up the groundwork for this program, this proposal aims to explore its practical implementation for the next generation of gravitational wave and galaxy surveys. This proposal is the continuation of an ambitious program that employs interdisciplinary and out-of-the-box thinking to push the frontiers of cosmology, and puts Canada in the forefront of scientific discovery. Students and Postdoctoral Researchers of diverse backgrounds are an integral part of this program, collaborating and contributing to an atmosphere of inquiry, innovation, and inclusivity. Meanwhile, they acquire invaluable and highly transferable skills, ranging from mathematical, numerical, and data science skills to analytic thinking and teamwork, enabling them to succeed and excel in a wide range of careers, from academia to industry and finance.