圈量子宇宙学中的微扰论研究

Loop quantum gravity (LQG) is one of the most promising candidates among quantum gravity theories. Loop quantum cosmology (LQC) inherited the quantization schemes originated from LQG to deal with the cosmological model, has met with great successes on the various cosmological problems. People have accumulated many accurate observation data for the cosmic microwave background. These data contain valuable information about the inflation, the structure formation of our universe and so on. The anisotropic fluctuation of the cosmic microwave background is described by the cosmological perturbation theory. In this proposal we plan to investigate the fluctuation of our universe with LQG. The comparison between the theoretical prediction and the experimental data helps us rule in or rule out possible quantization schemes in LQG, which can bring us important hint on the development of quantum gravity theory. Our proposal includes two parts. First, the possible quantization schemes in LQC will give theoretical prediction for power spectrum and non-Gaussianity. Second, with the comparison between the resulted theoretical prediction and the experimental observation, we can look for the quantum gravity signal in the cosmology observations and test the reliability of various quantization schemes in LQC.

圈量子引力理论是目前量子引力理论有力的候选者之一。圈量子宇宙学继承圈量子引力理论的量子化方式处理宇宙学模型，在宇宙学各种难题上展示了强有力的一面。宇宙微波背景的观测数据是宇宙学观测数据中数据量最丰富、精度最高的数据之一。该观测数据包含宇宙暴涨、大尺度结构形成等多种天文物理信息。理论上，影响宇宙微波背景各向异性的宇宙早期涨落对应宇宙学的微扰理论。本项目尝试将理论结果与实验数据相结合，用实验数据来限制模型中的参数。具体包括以下两个内容：一是针对宇宙微波背景辐射标量功率谱和非高斯性给出圈量子宇宙学的理论预言；二是把理论预言和实际的观测结果相比较，寻找量子宇宙学的可能观测效应并由此检验圈量子引力理论的合理性。

量子引力是基础物理学中的重要问题。圈量子引力理论作为量子引力理论的一个分支在过去的十多年时间里取得了重要的研究进展。特别是圈量子宇宙学，从理论框架层面解决了宇宙学原初的大爆炸奇点困难。如何从实验观测层面来检验圈量子宇宙学的理论结果是重要的和有趣的问题。该项目利用微扰论处理方法，考察圈量子宇宙学在各种宇宙学观测实验中可能留下的印迹，利用已有的实验数据对理论预言进行检验，或者提出可能的实验方案来检验圈量子宇宙学。另外，我们还把研究中得到的微扰论方法应用到全息原理，特别是AdS/CFT对应的研究中，取得了量子引力理论及其在超导物理中的应用的一系列成果。