非奇异宇宙学的有效场论及其可观测效应的研究

Inflation and the Hot Big Bang are past-incomplete, i.e., there exists an initial cosmological singularity. Since the known laws of physics at the singularity will become invalid, there is not sufficient physical motivation to set the initial state of perturbation modes to the lowest energy state of vacuum. An arbitrarily set initial state will not give the power spectrum of primordial scalar perturbations that is consistent with the observations. This requires a solution to the cosmological singularity problem, which includes not only the establishment of a nonsingular theory of cosmological evolution, but also the modification of gravity. Due to the existence of the “no-go” theorem, nonsingular cosmology based on the Horndeski theory cannot avoid instabilities in the perturbations. Therefore, it is of great significance to explore the theory of gravity that can establish healthy nonsingular cosmology. The effective field theory of cosmological perturbations inspires us to explore the healthy nonsingular cosmology in the beyond Horndeski theory. However, the current controversy about the choice of gauge still needs to be resolved, and the research on the validity of effective field theory and its observable effects still needs to be deepened. In this project, we will investigate the problems related to the gauge choice and the validity of the effective field theory in nonsingular cosmology. We will explore the observational effects of the nonsingular cosmology based on the stability of perturbations and the validity of the effective field theory. We expect to answer the significant scientific question on what is the theory of gravity that is needed for establishing healthy nonsingular cosmology.

暴涨和热大爆炸存在宇宙学初始奇点。奇点处已知的物理定律会失效，故将扰动初态设置为真空能量最低态缺乏足够的物理动机。任意设置的扰动初态将无法给出与观测相符的原初标量扰动功率谱。这要求我们解决宇宙学奇点问题，它既包括建立非奇异的宇宙学演化理论，也包括对引力理论的修改。由于止步定理的存在，基于 Horndeski 理论的非奇异宇宙学无法避免扰动不稳定性。因此，探索能够建立健康非奇异宇宙学的引力理论具有重要意义。宇宙学扰动的有效场论启示我们在超 Horndeski 理论下探索健康的非奇异宇宙学。然而，当前有关规范选择的争议仍然亟待解决，对有效场论有效性及其可观测效应的研究仍需深入。本项目中，我们将针对非奇异宇宙学中规范选择和有效场论有效性相关的问题展开调研，并探索基于扰动稳定性和有效场论有效性构建的非奇异宇宙学的可观测效应，以期回答“什么是健康的非奇异宇宙学所需要的引力理论”这一重要科学问题。

非奇异宇宙学有效场论的研究是深入理解宇宙学奇点问题和宇宙起源有关物理的一个重要途径。本项目紧密围绕非奇异宇宙学的有效场论及其可观测效应，主要从三个方面开展研究：一是结合弦理论中“沼泽地”猜想和超普朗克监督猜想的前沿进展，研究了暴涨和非奇异的反弹暴涨中扰动初始态的设置问题，探索了多阶段暴涨的可能性及相应有效场论需要满足的要求；二是研究了与非奇异宇宙学密切相关的零能量条件违反发生在极早期宇宙中的模型构建及其导致的原初引力波功率谱增强和相应的可观测效应；三是在幺正规范和空间平坦规范下，探索了微扰幺正性对于能够实现稳定零能量条件违反的非奇异宇宙学有效场论的限制与启示。这些研究工作从有效场论和扰动理论自洽性、极早期宇宙模型构建和原初引力波背景上的可观测效应等不同角度，在探索非奇异宇宙学相关的物理及其可观测效应方面取得了一定的进展，为未来进一步的深入研究打下了基础。

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