结合暗能量模型的观测限制及其贝叶斯模型选择标准解析暗能量性质

In the frame of general relativity, the dark energy theory has been one of the hot topic to explore the mechanism of present accelerated expansion of the Universe in modern cosmology. The solution of this problem strongly depends on the proper understanding of the nature of dark energy, meanwhile, one of the key methods to extract the nature of dark energy is to distinguish the theoretical models and assess the performance of dark energy models. This project will focus on the two aspects, one is to precisely constrain the cosmological parameters from the large-scale structure and future galaxy survey observations, the other is to assess the performance of dark energy models by the Bayesian model selection criterion. By combining the theoretical research, numerical simulation and cosmic observations, we will calculate the possible observational effects on the background expansion and large-scale structure formation of the Universe, employ the observational data to test the model parameter space, and calculate the Bayesian evidence of theoretical models by the nested sampling algorithm, and then assess the performance of dark energy models at the present precision, further, we could forecast the future galaxy surveys via Fisher matrix method so that the constraint precision of cosmological parameters would be improved, and Bayesian evidence of different theoretical models would be precisely calculated, then we can assess the performance of dark energy models at the high precision, this research of project would provide an important reference for extracting the nature of dark energy.

在广义相对论框架下利用暗能量理论探索当前宇宙加速膨胀机制是现代宇宙学研究的热点问题之一。该问题的解决极大地依赖于正确理解暗能量的性质，而区分不同暗能量模型并判断其优劣是解析暗能量性质的重要途径之一。本项目中，申请人将致力于大尺度结构观测和未来星系观测数据精确限制宇宙学参数以及贝叶斯模型选择标准判断模型优劣两方面开展工作。将理论研究、数值模拟和观测数据三者相结合，研究不同理论模型在宇宙背景膨胀和大尺度结构形成上的可观测效应，利用当前观测数据检验模型参数空间，通过嵌套取样算法计算贝叶斯证据并在当前观测精度上判断暗能量模型优劣；进一步，采用Fisher矩阵方法对未来星系巡天数据进行预测，据此提高宇宙学参数限制精度，并精确计算理论模型的贝叶斯证据，在高精度上判断暗能量模型优劣，为深入解析暗能量性质提供重要参考。

从理论研究、数值模拟和天文观测三个方面系统地研究了暗能量理论模型的观测限制及宇宙学模型选择机制，理论上通过对暗能量理论模型的分析，研究零阶背景演化方程和一阶扰动方程，分析不同理论模型对微波背景辐射各向异性功率谱、宇宙大尺度结构形成等方面的影响及所产生的可观测效应，结合最新发布的天文观测数据，采用马尔科夫链-蒙特卡洛计算方法给出模型参数的置信空间。将贝叶斯定理应用到宇宙学，利用嵌套取样算法修改适用于不同暗能量模型的宇宙学程序编码，便于在数值模拟程序中检验模型参数空间的同时，计算其贝叶斯证据。以贝叶斯定理为基础，以贝叶斯证据的计算结果为依据，利用大尺度结构观测和几何观测的联合数据在当前精度上确定不同暗能量理论模型的优劣，从当前观测数据中解析暗能量的性质。进一步，依据未来引力波探测计划的核心设计参数，模拟出引力波事件在不同红移处对应的光度距离及其误差，在未来引力波标准汽笛数据的更高精度上判断不同暗能量理论模型的优劣，深入解析暗能量的本质。